A155049 Expansion of (1+5*x)/(1-13*x+10*x^2).

1, 18, 224, 2732, 33276, 405268, 4935724, 60111732, 732095276, 8916121268, 108588623724, 1322490895732, 16106495407276, 196159531337268, 2389008953311724, 29095521079679732, 354351684502719276, 4315616687738553268, 52559500095573999724, 640117334365076463732

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..900

Tomislav Došlić and Frode Måløy, Chain hexagonal cacti: Matchings and independent sets, Discr. Math., 310 (2010), 1676-1690.

Index entries for linear recurrences with constant coefficients, signature (13,-10).

Formula

From Colin Barker, Jan 13 2020: (Start)

a(n) = 13*a(n-1) - 10*a(n-2) for n>1.

a(n) = 2^(-1-n)*((13-sqrt(129))^n*(-23+sqrt(129)) + (13+sqrt(129))^n*(23+sqrt(129))) / sqrt(129).

(End)

Mathematica

CoefficientList[Series[(1+5x)/(1-13x+10x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[{13, -10}, {1, 18}, 20] (* Harvey P. Dale, Mar 23 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (1+5*x)/(1-13*x+10*x^2) )); // Marius A. Burtea, Jan 13 2020
(Magma) a:=[1, 18]; [n le 2 select a[n] else 13*Self(n-1)-10*Self(n-2):n in [1..25]]; // Marius A. Burtea, Jan 13 2020
(PARI) Vec((1 + 5*x) / (1 - 13*x + 10*x^2) + O(x^20)) \\ Colin Barker, Jan 13 2020

Crossrefs

Sequence in context: A017997 A018911 A021194 * A155073 A153709 A017933

Adjacent sequences: A155046 A155047 A155048 * A155050 A155051 A155052

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2010

Status

approved