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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Programs

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 *)

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