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; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 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
(PARI) a(n)=n*(n+1)*(n^2-3*n+5)/6 \\ Charles R Greathouse IV, Oct 18 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Dennis S. Kluk (mathemagician(AT)ameritech.net)
STATUS
approved