A016130 Expansion of g.f. 1/((1-2*x)*(1-7*x)).

1, 9, 67, 477, 3355, 23517, 164683, 1152909, 8070619, 56494845, 395464939, 2768256621, 19377800443, 135644611293, 949512295435, 6646586100813, 46526102771227, 325682719529661, 2279779036969771, 15958453259312685, 111709172816237371, 781964209715758749, 5473749468014505547

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			1/((1-2*x)*(1-7*x)) = 1 + 9*x + 67*x^2 + 477*x^3 + 3355*x^4 + 23517*x^5 + 164683*x^6 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,-14).

Crossrefs

Cf. A190540.

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x) (1-7*x)))); // Vincenzo Librandi, Jun 24 2013

Mathematica

Join[{a=1,b=9},Table[c=9*b-14*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
CoefficientList[Series[1 /((1 - 2 x) (1 - 7 x)), {x, 0, 200}], x] (* Vincenzo Librandi, Jun 24 2013 *)

PARI

Vec(1/((1-2*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Sage

[lucas_number1(n,9,14) for n in range(1, 20)] # Zerinvary Lajos, Apr 23 2009

Sage

[(7^n - 2^n)/5 for n in range(1,20)] # Zerinvary Lajos, Jun 04 2009

Formula

a(n) = (7^(n+1) - 2^(n+1))/5. - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 06 2005

a(n) = 7*a(n-1) + 2^n, a(0)=1. - Vincenzo Librandi, Jun 24 2013

From Elmo R. Oliveira, Mar 27 2025: (Start)

E.g.f.: exp(2*x)*(7*exp(5*x) - 2)/5.

a(n) = A190540(n+1)/5.

a(n) = 9*a(n-1) - 14*a(n-2). (End)