A112502 Third column of triangle A112500.

1, 10, 60, 282, 1149, 4272, 14932, 49996, 162369, 515886, 1613316, 4987542, 15290461, 46592452, 141350412, 427459320, 1289718225, 3884883570, 11688205420, 35135919730, 105558754461, 316995030840, 951656181540

Offset

0,2

Comments

For a combinatorial formula see A112500, case k=3.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Formula

G.f.: 1/product((1-j*x)^(4-j), j=1..3) = 1/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).

a(n) = - 81/8 - (11/4)*(n+1) - (1/2)*binomial(n+2, 2) - 16*(n+1)*2^n + (243/8)*3^n, n>=0 (from partial fractions for g.f.).

Crossrefs

Cf. A000295 (second column).

Sequence in context: A341366 A004406 A003472 * A293081 A292489 A083585

Adjacent sequences: A112499 A112500 A112501 * A112503 A112504 A112505

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 14 2005

Status

approved