| Autor |
Beitrag |
    
sergi
| | Veröffentlicht am Montag, den 02. Juli, 2001 - 21:11: | 
|
Kennt jemand die Formel (explizit) der Folge:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55 .... ??? |
Marco
| | Veröffentlicht am Montag, den 02. Juli, 2001 - 21:33: |
|
Ja, starte mit n=0, dann ist die Formel:
(1/2)n2+(3/2)n+1
Habe mal eine Jugend-forscht-Arbeit über das Thema geschrieben, ist allerdings schon 19 Jahre her ;-) |
sergi
| | Veröffentlicht am Montag, den 02. Juli, 2001 - 23:02: |
|
danke , hast mir das leben gerettet !!!!
hab was ähnliches gefunden, bin aber dennoch nicht zum richtigen ergebnis gekommen...
danke nochmals :-) |
Fix&Foxi
| | Veröffentlicht am Dienstag, den 03. Juli, 2001 - 15:40: |
|
Hallo, auf http://www.research.att.com/~njas/sequences kamen nach der Eingabe von
1, 3, 6, 10, 15, 21, 28, 36, 45, 55
folgende Ausgaben:
Sequence: 0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,
190,210,231,253,276,300,325,351,378,406,435,465,496,528,561,
595,630,666,703,741,780,820,861,903,946,990,1035,1081,1128,
1176,1225,1275
Name: Triangular numbers: C(n+1,2) = n(n+1)/2.
Comments: a(n) = 0+1+2+...+n.
For n>=1 a(n)=n(n+1)/2 is also the genus of a nonsingular curve of
degree n+2 like the Fermat curve x^(n+2) + y^(n+2) = 1 - Ahmed Fares
(ahmedfares@my_deja.com), Feb 21 2001
a(n) is the number of ways in which (n+2) can be written as a sum of three
positive integers if representations differing in thr order of the
terms are considered to be different. In other words a(n) is the number
of positive integral solutions of the equation x + y + z = n+2.
1,3,6,10,15,21,28,36,45,55,66,78,92,107,123,140,158,177,197,
218,240,263,287,312,339,367,396,426,457,489,522,556,591,627,
664,703,743,784,826,869,913,958,1004,1051,1099,1148,1198,
1250,1303,1357,1412,1468,1525,1583
Name: Index of 7^n within sequence of numbers of form 6^i*7^j.
1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,137,155,174,194,
215,237,260,284,309,335,362,390,419,449,480,513,547,582,618,
655,693,732,772,813,855,898,942,987,1033,1081,1130,1180,
1231,1283,1336,1390,1445,1501,1558,1616
Name: Index of 8^n within sequence of numbers of form 7^i*8^j.
1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,191,
212,234,257,281,306,332,359,387,416,446,477,509,542,576,611,
647,684,723,763,804,846,889,933,978,1024,1071,1119,1168,
1218,1269,1321,1374,1428,1483,1540,1598
Name: Index of 9^n within sequence of numbers of form 8^i*9^j.
Sequence: 1,3,6,10,15,21,28,36,45,55,67,80,94,109,125,142,160,179,199,
221,244,268,293,319,346,374,403,433,465,498,532,567,603,640,
678,717,757,798,841,885,930,976,1023,1071,1120,1170,1221,
1274,1328,1383,1439,1496,1554,1613
Name: Index of 10^n within sequence of numbers of form 8^i*10^j.
Sequence: 1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,
210,231,254,278,303,329,356,384,413,443,474,506,539,573,608,
644,681,719,758,798,839,881,924,969,1015,1062,1110,1159,
1209,1260,1312,1365,1419,1474,1530,1587
Name: Index of 10^n within sequence of numbers of form 9^i*10^j.
0,0,1,3,6,10,15,21,28,36,45,55,65,76,88,101,115,130,146,163,
181,200,220,240,261,283,306,330,355,381,408,436,465,495,525,
556,588,621,655,690,726,763,801,840,880,920,961
Name: Number of edges in 11-partite Turan graph of order n.
References Graham et al., Handbook of Combinatorics, Vol 2, p. 1234.
Sequence: 0,0,1,3,6,10,15,21,28,36,45,55,66,77,89,102,116,131,147,164,
182,201,221,242,264,286,309,333,358,384,411,439,468,498,529,
561,594,627,661,696,732,769,807,846,886,927,969
Name: Number of edges in 12-partite Turan graph of order n.
1,3,6,10,15,21,28,36,45,55,66,77,90,104,119,134,151,169,188,
208,229,251,274,297,322,348,374,402,431,461,492,523,556,588,
623,658,695,733,771,810,851,893,936,980,1025,1071,1118,1164,
1213,1263,1313,1365,1417
Name: Number of distinct sums i^3 + j^3 for 1<=i<=j<=n.
Example: If the {s+t} sums are generated by addition 2 terms of an S set consisting
of n different entries, then at least 1, at most n(n+1)/2=A000217(n)
distinct values can be obtained. The set of first n cubes gives results
falling between these two extremes. E.g. S={1,8,27,...,2744,3375}
provides 119 different sums of two, not necessarily different
cubes:{2,9,....,6750}. Only a single sum occurs more then once:
1729(Ramanujan): 1729=1+1728=729+1000. |
|
