A018912 Expansion of 1/((1-4x)(1-5x)(1-10x)).

1, 19, 251, 2879, 30891, 320439, 3266131, 32986399, 331554971, 3324266759, 33287301411, 333100377519, 3332157369451, 33327408774679, 333303531583091, 3333183608754239, 33332581847126331, 333329564449052199

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-110,200).

Formula

a(n) = 8*4^n/3 - 5*5^n/1 + 10*10^n/3. - R. J. Mathar, Jun 29 2013

From Vincenzo Librandi, Jul 02 2013: (Start)

a(n) = 19*a(n-1) - 110*a(n-2) + 200*a(n-3) for n > 2; a(0)=1, a(1)=19, a(2)=251.

a(n) = 15*a(n-1) - 50*a(n-2) + 4^n. (End)

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2012 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-10*x)))); /* or */ I:=[1, 19, 251]; [n le 3 select I[n] else 19*Self(n-1)-110*Self(n-2)+200*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A021229 A021464 A017998 * A021202 A125454 A293917

Adjacent sequences: A018909 A018910 A018911 * A018913 A018914 A018915

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved