A003994 Sequence b_4 (n) arising from homology of partitions with even number of blocks.

6, 138, 1452, 11444, 78642, 502846, 3089624, 18559208, 110049502, 647720562, 3796113284, 22194147996, 129581349642, 755982695718, 4408534120368, 25702339082192, 149828229039030, 873339353640538, 5090437245730652

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

Cf. A003993.

Sequence in context: A367531 A245104 A075185 * A370734 A307353 A366227

Adjacent sequences: A003991 A003992 A003993 * A003995 A003996 A003997

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