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A006484 a(n) = n*(n + 1)*(n^2 - 3*n + 5)/6.
(Formerly M2839)
11
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; text; 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 07 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. - 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

D. S. Kluk and N. J. A. Sloane, Correspondence, 1979.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (1/6)*(n^4 - 2*n^3 + 2*n^2 + 5*n). - James A. Record (james.record(AT)gmail.com), Nov 07 2004

a(n) = binomial(n+3,4) - 2*binomial(n+2,4) + 5*binomial(n+1,4). - Johannes W. Meijer, Apr 29 2011

MAPLE

A006484:=-(1-2*z+5*z**2)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

lst={}; Do[AppendTo[lst, n*(n+1)*(n^2-3*n+5)/6], {n, 0, 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 19 2008 *)

Table[n(n+1) (n^2-3n+5)/6, {n, 0, 40}] (* Harvey P. Dale, May 29 2019 *)

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: A293155 A146384 A166174 * A144007 A026960 A026990

Adjacent sequences:  A006481 A006482 A006483 * A006485 A006486 A006487

KEYWORD

nonn

AUTHOR

Dennis S. Kluk (mathemagician(AT)ameritech.net)

STATUS

approved

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Last modified October 21 18:43 EDT 2019. Contains 328308 sequences. (Running on oeis4.)