A020346 Expansion of 1/((1-5x)(1-8x)(1-10x)).

1, 23, 359, 4747, 57351, 655683, 7229839, 77760587, 821694071, 8571599443, 88563029919, 908455411227, 9267399149191, 94137972490403, 953097676407599, 9624750893682667, 96997854561570711, 975982073553112563

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,-170,400).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-10*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 23, 359]; [n le 3 select I[n] else 23*Self(n-1)-170*Self(n-2)+400*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 10 x)),{x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

PARI

a(n) = 5^(n+1)/3-32*8^n/3+10^(n+1) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = 5^(n+1)/3 -4*8^(n+1)/3+10^(n+1). - R. J. Mathar, Mar 15 2011

a(0)=1, a(1)=23, a(2)=359; for n>2, a(n) = 23*a(n-1) -170*a(n-2) +400*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -80*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013