A016249 Expansion of 1/((1-x)*(1-7*x)*(1-8*x)).

1, 16, 185, 1880, 17841, 162336, 1435945, 12448360, 106312481, 897579056, 7510186905, 62388376440, 515255179921, 4235078618176, 34671889197065, 282913935338120, 2302083235036161, 18688068146607696, 151404361037090425, 1224533599346325400, 9889359772117817201

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (16,-71,56).

Crossrefs

Cf. A016218, A016228, A016241.

Programs

Mathematica

Table[(3*2^(3*n + 4) - 7^(n + 2) + 1)/42, {n, 40}] (* or *) CoefficientList[Series[1/((1 - z) (1 - 7*z) (1 - 8*z)), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)
LinearRecurrence[{16,-71,56},{1,16,185},30] (* Harvey P. Dale, May 14 2023 *)

PARI

Vec(1/((1-x)*(1-7*x)*(1-8*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(0)=1, a(1)=16, a(n) = 15*a(n-1) - 56*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011