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

0,2

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).

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)

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 *)

Prog

(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

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)

Sequence in context: A041620 A375329 A244879 * A298275 A299137 A299368

Adjacent sequences: A142962 A142963 A142964 * A142966 A142967 A142968

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 15 2008

Status

approved