A016207 Expansion of g.f. 1/((1-x)*(1-2*x)*(1-12*x)).

1, 15, 187, 2259, 27139, 325731, 3908899, 46907043, 562885027, 6754621347, 81055458211, 972665502627, 11671986039715, 140063832492963, 1680765989948323, 20169191879445411, 242030302553476003, 2904363630641974179, 34852363567704214435, 418228362812451621795

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (15,-38,24).

Formula

a(n) = (72*12^n - 22*2^n + 5)/55. - Bruno Berselli, Feb 09 2011

a(n) = 12*a(n-1) + 2^(n+1) - 1, n>0. - Vincenzo Librandi, Feb 09 2011

From Elmo R. Oliveira, Jul 06 2025: (Start)

a(n) = A016136(n+1) - A016125(n+1).

a(n) = 15*a(n-1) - 38*a(n-2) + 24*a(n-3).

E.g.f.: exp(x)*(5 - 22*exp(x) + 72*exp(11*x))/55. (End)

Maple

A016207 := proc(n) (6*12^(n+1)-11*2^(n+1)+5)/55 ; end proc:
seq(A016207(n), n=0..20) ; # R. J. Mathar, Feb 09 2011

Mathematica

A016207[n_] := (72*12^n - 22*2^n + 5)/55; Array[A016207, 20, 0] (* Paolo Xausa, Feb 08 2024 *)
(* Alternative: *)
LinearRecurrence[{15, -38, 24}, {1, 15, 187}, 20] (* Paolo Xausa, Feb 08 2024 *)

Prog

(PARI) Vec(1/((1-x)*(1-2*x)*(1-12*x))+O(x^20)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A016125, A016136.

Sequence in context: A387366 A240796 A206514 * A286347 A016147 A145601

Adjacent sequences: A016204 A016205 A016206 * A016208 A016209 A016210

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved