OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (15, -59, 45).
FORMULA
a(0)=1, a(1)=15, a(n) = 14*a(n-1) - 45*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011
a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32. - Yahia Kahloune, Aug 13 2013
a(0)=1, a(1)=15, a(2)=166, a(n) = 15*a(n-1) - 59*a(n-2) + 45*a(n-3). - Harvey P. Dale, Oct 16 2014
O.g.f.: see the name.
E.g.f.: (d^2/dx^2) (exp(x)*((exp(4*x) - 1)^2)/(4^2*2!)) = exp(x)*(1 - 50*exp(4*x) + 81*exp(8*x))/32.
MATHEMATICA
CoefficientList[Series[1/((1-x)(1-5x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{15, -59, 45}, {1, 15, 166}, 30] (* Harvey P. Dale, Oct 16 2014 *)
PROG
(PARI) Vec(1/((1-x)*(1-5*x)*(1-9*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
(PARI) a(n) = (9^(n+2) - 2*5^(n+2) + 1)/32; \\ Joerg Arndt, Aug 13 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved