A016239 Expansion of 1/((1-x)*(1-5*x)*(1-12*x)).

1, 18, 247, 3120, 38221, 462558, 5570227, 66940380, 803772841, 9647715498, 115784793007, 1389478551240, 16674047790661, 200090099366838, 2401088821796587, 28813104008531700, 345757438837243681

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (18,-77,60).

Formula

a(0)=1, a(1)=18; for n>1, a(n)=17*a(n-1)-60*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308. - Yahia Kahloune, Aug 13 2013

E.g.f.: (1/308)*(7*exp(x) - 275*exp(5*x) + 576*exp(12*x)). - G. C. Greubel, Jan 30 2022

Mathematica

LinearRecurrence[{18, -77, 60}, {1, 18, 247}, 40] (* G. C. Greubel, Jan 30 2022 *)

Prog

(PARI) a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308; \\ Joerg Arndt, Aug 13 2013
(Magma) [(4*12^(n+2) -11*5^(n+2) +7)/308: n in [0..40]]; // G. C. Greubel, Jan 30 2022
(Sage) [(4*12^(n+2) -11*5^(n+2) +7)/308 for n in (0..40)] # G. C. Greubel, Jan 30 2022

Crossrefs

Cf. A003463, A016238.

Sequence in context: A110395 A153600 A016183 * A153886 A154241 A154250

Adjacent sequences: A016236 A016237 A016238 * A016240 A016241 A016242

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved