A020341 Expansion of 1/((1-5x)(1-7x)(1-12x)).

1, 24, 397, 5652, 74665, 946992, 11736613, 143526444, 1741517569, 21034565640, 253379036989, 3047347017156, 36615998359513, 439728040092768, 5279095003079125, 63365680208288988, 760504096286734897

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 (24,-179,420)

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-7*x)*(1-12*x)))); // Vincenzo Librandi, Jul 03 2013

Magma

I:=[1, 24, 397]; [n le 3 select I[n] else 24*Self(n-1)-179*Self(n-2)+420*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Mathematica

CoefficientList[Series[1/((1-5x)(1-7x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{24,-179,420},{1,24,397},30] (* Harvey P. Dale, Dec 10 2011 *)

Formula

a(n) = 5^(n+2)/14 -7^(n+2)/10 +12^(n+2)/35. - R. J. Mathar, Mar 15 2011

a(0)=1, a(1)=24, a(2)=397, a(n)=24*a(n-1)-179*a(n-2)+420*a(n-3). [Harvey P. Dale, Dec 10 2011]

a(n) = 19*a(n-1) -84*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013