A016313 Expansion of 1/((1-2*x)*(1-7*x)*(1-10*x)).

1, 19, 257, 3047, 33825, 361767, 3782353, 38976439, 397835009, 4034844935, 40743914289, 410207399511, 4121451795553, 41350162566823, 414451137963665, 4151157965737463, 41558105760145857, 415906740320988231

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 (19,-104,140).

Programs

Magma

I:=[1, 19, 257]; [n le 3 select I[n] else 19*Self(n-1)-104*Self(n-2) +140*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 26 2013

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-7*x)*(1-10*x)))); // Vincenzo Librandi, Jun 26 2013

Mathematica

CoefficientList[Series[1/((1-2x)(1-7x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{19,-104,140},{1,19,257},30] (* Harvey P. Dale, May 02 2012 *)

PARI

Vec(1/((1-2*x)*(1-7*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(0)=1, a(1)=19, a(2)=257, a(n)=19*a(n-1)-104*a(n-2)+140*a(n-3). - Harvey P. Dale, May 02 2012

a(n) = 2^n/10 - 49*7^n/15 + 25*10^n/6. - R. J. Mathar, Jun 23 2013

a(n) = 17*a(n-1) - 70*a(n-2) + 2^n. - Vincenzo Librandi, Jun 26 2013