A020594 Expansion of 1/((1-6x)(1-8x)(1-12x)).

1, 26, 460, 6920, 95536, 1254176, 15958720, 199053440, 2450711296, 29915173376, 363095649280, 4390419138560, 52953377222656, 637600367845376, 7668561507696640, 92162065025761280, 1107062216886255616

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (26,-216,576).

Formula

a(n) = (2*12^(n+2) - 6*8^(n+2) + 4*6^(n+2))/48. [Yahia Kahloune, Jun 30 2013]

a(0)=1, a(1)=26, a(2)=460; for n>2, a(n) = 26*a(n-1) -216*a(n-2) +576*a(n-3). - Vincenzo Librandi, Jul 04 2013

a(n) = 20*a(n-1) -96*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 6 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 04 2013 *)
LinearRecurrence[{26, -216, 576}, {1, 26, 460}, 20] (* Harvey P. Dale, Nov 10 2021 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1, 26, 460]; [n le 3 select I[n] else 26*Self(n-1)-216*Self(n-2)+576*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A158430 A158435 A158424 * A158437 A158429 A158434

Adjacent sequences: A020591 A020592 A020593 * A020595 A020596 A020597

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved