A016147 Expansion of 1/((1-3*x)*(1-12*x)).

1, 15, 189, 2295, 27621, 331695, 3981069, 47775015, 573306741, 6879700575, 82556465949, 990677768535, 11888133753861, 142657606640655, 1711891284470829, 20542695427998855, 246512345179032981, 2958148142277535935, 35497777707717851709, 425973332493776481975

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (15,-36).

Formula

a(n) = 15*a(n-1) - 36*a(n-2). - Vincenzo Librandi, Mar 14 2011

a(n) = (4*12^n - 3^n)/3. - Zak Seidov, Mar 14 2011

E.g.f.: exp(3*x)*(4*exp(9*x) - 1)/3. - Elmo R. Oliveira, Mar 08 2025

Mathematica

Join[{a=1, b=15}, Table[c=15*b-36*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{15, -36}, {1, 15}, 20] (* Harvey P. Dale, Apr 30 2013 *)

Crossrefs

Sequence in context: A206514 A016207 A286347 * A145601 A004344 A038339

Adjacent sequences: A016144 A016145 A016146 * A016148 A016149 A016150

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved