A142965 One fourth of third column (m=2) of triangle A142963.

1, 18, 129, 646, 2685, 10002, 34777, 115566, 372453, 1175290, 3654369, 11245110, 34349005, 104373282, 315969705, 954002878, 2874983541, 8652474378, 26015617585, 78169534470, 234766551261, 704840716978, 2115654610809, 6349329417486, 19052920751365, 57169029907482

Offset: 0

Author

Wolfdieter Lang, Sep 15 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10, -40, 82, -91, 52, -12).

Crossrefs

Column m=1: 2*A142964; m=3: 8*A142966.

From Johannes W. Meijer, Feb 20 2009: (Start)

Cf. A156925.

Equals A156920(n+2,2).

Equals A156919(n+2,2)/2^n.

(End)

Programs

Magma

[35/2+2*n^2+12*n-84*2^n-24*2^n*n+135/2*3^n: n in [0..25]]; // Vincenzo Librandi, Jun 18 2017

Mathematica

LinearRecurrence[{10,-40,82,-91,52,-12}, {1,18,129,646,2685,10002},30] (* or *) CoefficientList[Series[(1+8x-11x^2-6x^3)/((x-1)^3 (2x-1)^2 (3x-1)),{x,0,30}],x] (* Harvey P. Dale, Apr 24 2011 *)

Formula

a(n) = A142963(n+3,2)/4.

From Johannes W. Meijer, Feb 20 2009: (Start)

a(n) = 10a(n-1) - 40a(n-2) + 82a(n-3) - 91a(n-4) + 52a(n-5) - 12a(n-6).

a(n) = 35/2 + 2*n^2 + 12*n - 84*2^n - 24*2^n*n + 135/2*3^n

G.f.: (1 + 8*z - 11*z^2 - 6*z^3)/((1-z)^3*(1-2*z)^2*(1-3*z)).

(End)