A016166 Expansion of 1/((1-5*x)*(1-12*x)).

1, 17, 229, 2873, 35101, 424337, 5107669, 61370153, 736832461, 8843942657, 106137077509, 1273693758233, 15284569239421, 183416051576177, 2200998722429749, 26412015186735113, 316944334828711981, 3803332780883996897, 45639997185305228389, 547679985297149068793

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..920
• Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seqs., Vol. 6, 2003.
• Index entries for linear recurrences with constant coefficients, signature (17,-60).

Crossrefs

Cf. A016161.

Programs

Magma

[(12^(n+1)-5^(n+1))/7 : n in [0..30]]; // Wesley Ivan Hurt, Aug 28 2015

Maple

A016166:=n->(12^(n+1)-5^(n+1))/7: seq(A016166(n), n=0..30); # Wesley Ivan Hurt, Aug 28 2015

Mathematica

LinearRecurrence[{17,-60}, {1,17}, 41] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
Table[(12^(n+1)-5^(n+1))/7, {n,0,40}] (* Wesley Ivan Hurt, Aug 28 2015 *)

SageMath

A016166=BinaryRecurrenceSequence(17,-60,1,17)
[A016166(n) for n in range(41)] # G. C. Greubel, Nov 10 2024

Formula

G.f.: 1/((1-5*x)*(1-12*x)).

a(n) = (12^(n+1) - 5^(n+1))/7. - Bruno Berselli, Feb 09 2011

a(n) = 12*a(n-1) + 5^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011

a(n) = 17*a(n-1) - 60*a(n-2), n > 1. - Wesley Ivan Hurt, Aug 28 2015

E.g.f.: (1/7)*(12*exp(12*x) - 5*exp(5*x)). - G. C. Greubel, Nov 10 2024