A021344 Expansion of 1/((1-x)*(1-3*x)*(1-4*x)*(1-5*x)).

1, 13, 110, 770, 4851, 28623, 161680, 885940, 4749701, 25058033, 130616850, 674656710, 3460370551, 17652592243, 89673093620, 454027521080, 2292850387401, 11555296775253, 58141244359990

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-59,107,-60).

Formula

a(0)=1, a(1)=13, a(2)=110, a(3)=770; for n>3, a(n) = 13*a(n-1) -59*a(n-2) +107*a(n-3)-60*a(n-4). - Vincenzo Librandi, Jul 09 2013

a(0)=1, a(1)=13; for n>1, a(n) = 9*a(n-1) -20*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 - 5 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 09 2013 *)
LinearRecurrence[{13, -59, 107, -60}, {1, 13, 110, 770}, 20] (* Harvey P. Dale, May 10 2024 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-5*x)))); // Vincenzo Librandi, Jul 09 2013
(Magma) I:=[1, 13, 110, 770]; [n le 4 select I[n] else 13*Self(n-1)-59*Self(n-2)+107*Self(n-3)-60*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 09 2013

Crossrefs

Sequence in context: A075143 A005769 A042941 * A119744 A295204 A298228

Adjacent sequences: A021341 A021342 A021343 * A021345 A021346 A021347

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved