A019682 Expansion of 1/((1-4*x)*(1-9*x)*(1-10*x)).

1, 23, 363, 4891, 60515, 710619, 8059507, 89191307, 969344739, 10390594555, 110181318611, 1158295737963, 12091317123523, 125488476039131, 1296062772061875, 13331230899395659, 136647741897916067, 1396496332294665147, 14235133611505668499, 144782868986965745195

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (23,-166,360).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-9*x)*(1-10*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 23, 363]; [n le 3 select I[n] else 23*Self(n-1)-166*Self(n-2)+360*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [23, -166, 360][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

PARI

Vec(1/((1-4*x)*(1-9*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = -9^(n+2)/5 +5*10^(n+1)/3+2*4^(n+1)/15. - R. J. Mathar, Mar 15 2011

a(0)=1, a(1)=23, a(2)=363; for n>2, a(n) = 23*a(n-1) -166*a(n-2) +360*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 19*a(n-1) -90*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013