A020606 Expansion of g.f. 1/((1-6*x)*(1-9*x)*(1-11*x)).

1, 26, 457, 6782, 91693, 1170218, 14373409, 171896534, 2016642805, 23325176930, 266916367081, 3029497622606, 34167408893437, 383440973924762, 4286324362209073, 47766301010614598, 530982729463501189, 5890807715878623314, 65248965660642516985, 721789958700606642110

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (26,-219,594).

Formula

a(0)=1, a(1)=26, a(2)=457, a(n) = 26*a(n-1)-219*a(n-2)+594*a(n-3). [Harvey P. Dale, Oct 26 2011]

a(n) = (3*11^(n+2) - 5*9^(n+2) + 2*6^(n+2))/30. [Yahia Kahloune, Jun 30 2013]

a(n) = 20*a(n-1) -99*a(n-2) +6^n. - Vincenzo Librandi, Jul 04 2013

Mathematica

CoefficientList[Series[1 / ((1 - 6 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{26, -219, 594}, {1, 26, 457}, 20] (* Harvey P. Dale, Oct 26 2011 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-9*x)*(1-11*x)))); // Vincenzo Librandi, Jul 04 2013
(Magma) I:=[1, 26, 457]; [n le 3 select I[n] else 26*Self(n-1)-219*Self(n-2)+594*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A020968 A025955 A022725 * A021984 A025954 A158436

Adjacent sequences: A020603 A020604 A020605 * A020607 A020608 A020609

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved