A003993 Sequence b_3 (n) arising from homology of partitions with even number of blocks.

2, 12, 46, 152, 474, 1444, 4358, 13104, 39346, 118076, 354270, 1062856, 3188618, 9565908, 28697782, 86093408, 258280290, 774840940, 2324522894, 6973568760, 20920706362, 62762119172, 188286357606, 564859072912, 1694577218834, 5083731656604, 15251194969918

Offset

2,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..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 (5,-7,3).

Formula

a(n) = 2*3^(n-1)-2*n. - Vaclav Kotesovec, Nov 19 2012

From Colin Barker, Jun 20 2019: (Start)

G.f.: 2*x^2*(1 + x) / ((1 - x)^2*(1 - 3*x)).

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3) for n>4.

(End)

Maple

A003993 := proc(n) option remember; if n = 1 then 2 else 3*A003993(n-1)+4*n-2; fi; end;

Mathematica

Table[2 3^(n-1) - 2 n, {n, 2, 30}] (* Vincenzo Librandi, May 03 2013 *)

Prog

(Magma) [2*3^(n-1)-2*n: n in [2..30]]; // Vincenzo Librandi, May 03 2013
(PARI) Vec(2*x^2*(1 + x) / ((1 - x)^2*(1 - 3*x)) + O(x^40)) \\ Colin Barker, Jun 20 2019

Crossrefs

Cf. A003994.

Sequence in context: A188982 A061990 A006742 * A129018 A302447 A319763

Adjacent sequences: A003990 A003991 A003992 * A003994 A003995 A003996

Keyword

nonn,easy

Author

Sheila Sundaram (sheila(AT)paris-gw.cs.miami.edu)

Status

approved