A016633 Expansion of g.f. 1/((1-2*x)*(1-11*x)*(1-12*x)).

1, 25, 447, 6989, 101759, 1417941, 19180519, 253983853, 3309800367, 42599540357, 542895780791, 6863463633117, 86197420501375, 1076563471968373, 13382900349107463, 165700329729679181, 2044564737700501583, 25152545442794015589, 308625999807796411735, 3778261997130507936445

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (25,-178,264).

Crossrefs

Cf. A006516, A016127, A016129, A016130, A016311, A016316, A016321, A016325. - Zerinvary Lajos, Jun 05 2009

Cf. A016135, A016136.

Programs

Magma

[(648*12^n +2^(n+1)-5*11^(n+2))/45 : n in [0..20]]; // Vincenzo Librandi, Oct 09 2011

Mathematica

CoefficientList[Series[1/((1 - 2 x) (1 - 11 x) (1 - 12 x)), {x, 0, 15}], x] (* Michael De Vlieger, Jan 31 2018 *)

PARI

Vec(1/((1-2*x)*(1-11*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[(12^n - 2^n)/10-(11^n - 2^n)/9 for n in range(2,18)] # Zerinvary Lajos, Jun 05 2009

Formula

From Vincenzo Librandi, Oct 09 2011: (Start)

a(n) = (648*12^n + 2^(n+1) - 5*11^(n+2))/45.

a(n) = 23*a(n-1) - 132*a(n-2) + 2^n.

a(n) = 25*a(n-1) - 178*a(n-2) + 264*a(n-3), n >= 3. (End)

From Elmo R. Oliveira, Mar 26 2025: (Start)

E.g.f.: exp(2*x)*(648*exp(10*x) - 605*exp(9*x) + 2)/45.

a(n) = A016136(n+1) - A016135(n+1). (End)