OFFSET
3,1
LINKS
Ray Chandler, Table of n, a(n) for n = 3..1000
S. Sundaram, The homology of partitions with an even number of blocks, J. Alg. Comb., 4 (1995), 69-92.
S. Sundaram, Plethysm, partitions with an even number of blocks and Euler numbers, DIMACS Series, Vol. 24 (1996), 171-198, Amer. Math. Soc.
Index entries for linear recurrences with constant coefficients, signature (15,-85,235,-339,253,-87,9).
FORMULA
a(n) = 6*a(n-1) - a(n-2) - 8*n^2 + 24*n - 10 + 3^(n-3)*(32*n-80), with a(1)=a(2)=0. - Sean A. Irvine, Sep 26 2015
From Colin Barker, Jun 20 2019: (Start)
G.f.: 2*x^3*(3 + 24*x - 54*x^2 - 8*x^3 + 3*x^4) / ((1 - x)^3*(1 - 3*x)^2*(1 - 6*x + x^2)).
a(n) = 15*a(n-1) - 85*a(n-2) + 235*a(n-3) - 339*a(n-4) + 253*a(n-5) - 87*a(n-6) + 9*a(n-7) for n>9.
a(n) = (-12 + 16*3^n - 3*(3-2*sqrt(2))^n*(-2+sqrt(2)) + 6*(3+2*sqrt(2))^n + 3*sqrt(2)*(3+2*sqrt(2))^n - 16*(3+2*3^n)*n + 48*n^2) / 24.
(End)
Colin Barker's conjecture confirmed by Sean A. Irvine's formula. - Ray Chandler, Jul 06 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Sheila Sundaram (sheila(AT)paris-gw.cs.miami.edu)
EXTENSIONS
More terms added and incorrect Maple code deleted by Sean A. Irvine, Sep 26 2015
STATUS
approved