A016765 Expansion of 1/((1-3*x)*(1-4*x)*(1-6*x)).

1, 13, 115, 865, 5971, 39193, 249355, 1555105, 9573091, 58428073, 354585595, 2143759345, 12928070611, 77832076153, 468051849835, 2812563019585, 16892428846531, 101422905135433, 608811146458075, 3653962903591825, 21928165007708851, 131586550851237913

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-54,72).

Formula

a(n) = 6^(n+1) - 2^(2*n+3) + 3^(n+1). - Vincenzo Librandi, Mar 20 2011

a(n) = 10*a(n-1) - 24*a(n-2) + 3^n, n >= 2. - Vincenzo Librandi, Mar 20 2011

G.f.: 1/((1-3*x)*(1-4*x)*(1-6*x)) = -3/(1-3*x) + 8/(1-4*x) - 6/(1-6*x). - Wolfdieter Lang, May 19 2014

Maple

A016765:=n->6^(n+1)-2^(2*n+3)+3^(n+1); seq(A016765(n), n=0..20); # Wesley Ivan Hurt, May 15 2014

Mathematica

Table[6^(n + 1) - 2^(2*n + 3) + 3^(n + 1), {n, 0, 20}] (* Wesley Ivan Hurt, May 15 2014 *)
CoefficientList[Series[1/((1-3x)(1-4x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, -54, 72}, {1, 13, 115}, 30] (* Harvey P. Dale, Jul 18 2021 *)

Prog

(Magma) [6^(n+1)-2^(2*n+3)+3^(n+1): n in [0..20]]; // Wesley Ivan Hurt, May 15 2014
(PARI) vector(30, n, n--; 6^(n+1)-2^(2*n+3)+3^(n+1)) \\ G. C. Greubel, Sep 15 2018

Crossrefs

Sequence in context: A320617 A156969 A287471 * A362514 A115188 A155621

Adjacent sequences: A016762 A016763 A016764 * A016766 A016767 A016768

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1999

Status

approved