A021404 Expansion of 1/((1-x)(1-3x)(1-4x)(1-12x)).

1, 20, 285, 3640, 44681, 540540, 6505045, 78138080, 937976961, 11257033060, 135089723405, 1621098253320, 19453266126841, 233439544261580, 2801275941271365, 33615316957309360, 403383826200494321

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-115,240,-144).

Formula

a(0)=1, a(1)=20, a(2)=285, a(3)=3640, a(n) = 20*a(n-1)-115*a(n-2)+240*a(n-3)- 144*a(n-4). [Harvey P. Dale, May 06 2012]

a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -48*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 09 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{20, -115, 240, -144}, {1, 20, 285, 3640}, 30] (* Harvey P. Dale, May 06 2012 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-12*x)))); /* or */ I:=[1, 20, 285, 3640]; [n le 4 select I[n] else 20*Self(n-1)-115*Self(n-2)+240*Self(n-3)-144*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A021204 A017953 A016317 * A046175 A231105 A016314

Adjacent sequences: A021401 A021402 A021403 * A021405 A021406 A021407

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved