A020766 Expansion of g.f. 1/((1-6*x)*(1-11*x)*(1-12*x)).

1, 29, 571, 9521, 144907, 2083865, 28847827, 388709777, 5134091323, 66784487561, 858403625443, 10928093824193, 138039056180299, 1732402968047417, 21624191213455219, 268679676312195569, 3325242136114316635, 41014868784078912233, 504410121626681853955, 6187470727275006236705

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (29,-270,792).

Crossrefs

Cf. A016174, A016175.

Programs

Mathematica

CoefficientList[Series[1/((1-6x)(1-11x)(1-12x)),{x,0,20}],x] (* or *) LinearRecurrence[{29,-270,792},{1,29,571},20] (* Harvey P. Dale, Jun 13 2015 *)

Formula

a(n) = 23*a(n-1) - 132*a(n-2) + 6^n; a(0)=1, a(1)=29. - Vincenzo Librandi, Mar 11 2011

a(n) = 6*6^n/5 - 121*11^n/5 + 24*12^n. - R. J. Mathar, Jul 01 2013

a(n) = 29*a(n-1) - 270*a(n-2) + 792*a(n-3); a(0)=1, a(1)=29, a(2)=571. - Harvey P. Dale, Jun 13 2015

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

E.g.f.: exp(6*x)*(6 - 121*exp(5*x) + 120*exp(6*x))/5.

a(n) = A016175(n+1) - A016174(n+1). (End)

Extensions

More terms from Elmo R. Oliveira, Mar 26 2025