A021534 Expansion of 1/((1-x)(1-3x)(1-6x)(1-12x)).

1, 22, 337, 4522, 57253, 705334, 8574889, 103567234, 1246828045, 14986093486, 179978152081, 2160608272186, 25932522746677, 311221616234278, 3734847461630713, 44819297962008178, 537838346143305949

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-147,342,-216).

Formula

a(0)=1, a(1)=22; for n>1, a(n) = 18*a(n-1) -72*a(n-2) +(3^n - 1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=22, a(2)=337, a(3)=4522; for n>3, a(n) = 22*a(n-1) -147*a(n-2) +342*a(n-3) -216*a(n-4). - Vincenzo Librandi, Jul 11 2013

a(n) = -1/110-(12/5)*6^n+(1/2)*3^n+(32/11)*12^n - Robert Israel, Apr 06 2014

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)
LinearRecurrence[{22, -147, 342, -216}, {1, 22, 337, 4522}, 20] (* Harvey P. Dale, Mar 05 2019 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-12*x)))); /* or */ I:=[1, 22, 337, 4522]; [n le 4 select I[n] else 22*Self(n-1)-147*Self(n-2)+342*Self(n-3)-216*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013

Crossrefs

Sequence in context: A223812 A018090 A021274 * A018070 A332873 A019490

Adjacent sequences: A021531 A021532 A021533 * A021535 A021536 A021537

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved