A022448 Expansion of 1/((1-x)*(1-5*x)*(1-6*x)*(1-12*x)).

1, 24, 391, 5466, 71017, 888660, 10902187, 132353502, 1597893853, 19235078616, 231195264703, 2776650139458, 33333948627409, 400093791131292, 4801651568584339, 57623013420037734, 691495519357470085, 8298063335866061088, 99577467420222835495, 1194933877223512550730

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-185,522,-360)

Formula

a(n) = 125*5^n/28 -36*6^n/5 +288*12^n/77 -1/220.

a(0)=1, a(1)=24, a(2)=391, a(3)=5466; for n>3, a(n) = 24*a(n-1) -185*a(n-2) +522*a(n-3) -360*a(n-4). - Vincenzo Librandi, Jul 12 2013

Maple

A022448:=n->125*5^n/28 - 36*6^n/5 + 288*12^n/77 - 1/220; seq(A022448(n), n=0..20); # Wesley Ivan Hurt, Feb 15 2014

Mathematica

CoefficientList[Series[1/((1-x)*(1-5*x)*(1-6*x)*(1-12*x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)

Prog

(Magma) I:=[1, 24, 391, 5466]; [n le 4 select I[n] else 24*Self(n-1)-185*Self(n-2)+522*Self(n-3)-360*Self(n-4): n in [1..25]]; /* or */  m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-6*x)*(1-12*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-6*x)*(1-12*x))) \\ G. C. Greubel, Feb 28 2018

Crossrefs

Sequence in context: A021924 A020494 A020573 * A025947 A007752 A145602

Adjacent sequences: A022445 A022446 A022447 * A022449 A022450 A022451

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved