|
| |
|
|
A006484
|
|
n*(n+1)*(n^2 - 3*n + 5)/6.
(Formerly M2839)
|
|
8
| |
|
|
0, 1, 3, 10, 30, 75, 161, 308, 540, 885, 1375, 2046, 2938, 4095, 5565, 7400, 9656, 12393, 15675, 19570, 24150, 29491, 35673, 42780, 50900, 60125, 70551, 82278, 95410, 110055, 126325, 144336, 164208, 186065, 210035, 236250, 264846, 295963, 329745, 366340
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Structured meta-pyramidal numbers, the n-th number from an n-gonal pyramidal number sequence. - James A. Record (james.record(AT)gmail.com). Nov. 7, 2004.
The Gi4 triangle sums of A139600 are given by the terms of this sequence. For the definitions of the Gi4 and other triangle sums see A180662. [From Johannes W. Meijer, Apr 29 2011]
|
|
|
REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
|
FORMULA
| a(n)=(1/6)*(n^4-2*n^3+2*n^2+5*n). - James A. Record (james.record(AT)gmail.com). Nov. 7, 2004.
a(n) = binomial(n+3,4) - 2*binomial(n+2,4) + 5*binomial(n+1,4). [From Johannes W. Meijer, Apr 29 2011]
|
|
|
MAPLE
| A006484:=-(1-2*z+5*z**2)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
|
MATHEMATICA
| lst={}; Do[AppendTo[lst, n*(n+1)*(n^2-3*n+5)/6], {n, 0, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 19 2008]
|
|
|
PROG
| (MAGMA) [n*(n+1)*(n^2 - 3*n + 5)/6: n in [0..50]]; // Vincenzo Librandi, May 16 2011
|
|
|
CROSSREFS
| Cf. other meta sequences: A100177: prism; A000447: "polar" diamond; A059722: "equatorial diamond"; A100185: anti-prism; A100188: "polar" anti-diamond; and A100189: "equatorial" anti-diamond. Cf. A100145 for more on structured numbers.
Cf. A000332.
Sequence in context: A147062 A146384 A166174 * A144007 A026960 A026990
Adjacent sequences: A006481 A006482 A006483 * A006485 A006486 A006487
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Dennis S. Kluk (mathemagician(AT)ameritech.net)
|
| |
|
|
