A018207 Expansion of 1/((1-3x)(1-10x)(1-12x)).

1, 25, 439, 6685, 94471, 1276405, 16745119, 215226205, 2725568791, 34135388485, 423910350799, 5229781276525, 64185946519111, 784517071831765, 9557062002788479, 116113315455883645, 1407645499737869431

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (25,-186,360).

Programs

Magma

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-10*x)*(1-12*x)))); // Vincenzo Librandi, Jul 02 2013

Magma

I:=[1, 25, 439]; [n le 3 select I[n] else 25*Self(n-1)-186*Self(n-2)+360*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{25,-186,360},{1,25,439},20] (* Harvey P. Dale, Jul 20 2022 *)

Formula

a(0)=1, a(1)=25, a(2)=439; for n>2. a(n) = 25*a(n-1) -186*a(n-2) +360*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 22*a(n-1) -120*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

a(n) = (7*12^(n+2) - 9*10^(n+2) + 2*3^(n+2))/126. [Yahia Kahloune, Jul 06 2013]