OFFSET
0,6
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 17.
G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, European Journal of Combinatorics, Vol. 22, No. 7 (2001), 887-904.
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
G.f.: q^4/(1-q)^4-4*q^7/(1-q)^4/(1+q)^3.
a(n) = (2*n^3-3*n^2-23*n+3*(13+(n^2-7*n+11)*(-1)^n))/24. - Luce ETIENNE, Jul 02 2015; edited by Mo Li, Sep 18 2019
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7. - Colin Barker, Sep 18 2019
MATHEMATICA
Table[Piecewise[{
{Binomial[k - 1, k - 4] - 4*Binomial[(k - 1)/2, (k - 7)/2], Mod[k, 2] == 1},
{Binomial[k - 1, k - 4] - 4*Binomial[(k - 2)/2, (k - 8)/2], Mod[k, 2] == 0}}], {k, 1, 20}] (* Mo Li, Sep 18 2019 *)
PROG
(PARI) concat([0, 0, 0, 0], Vec(x^4*(1 + 3*x + 3*x^2 - 3*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, Sep 18 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 06 2002
STATUS
approved