A155542 Expansion of (2+2*x)/(1-8*x-25*x^2).

2, 18, 194, 2002, 20866, 216978, 2257474, 23484242, 244310786, 2541592338, 26440508354, 275063875282, 2861523711106, 29768786570898, 309688385344834, 3221726747031122, 33516023609869826, 348671357554736658, 3627271450684638914, 37734955544345527762

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..950

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 (8,25).

Formula

From Colin Barker, Jan 13 2020: (Start)

a(n) = 8*a(n-1) + 25*a(n-2) for n>1.

a(n) = ((4-sqrt(41))^n*(-5+sqrt(41)) + (4+sqrt(41))^n*(5+sqrt(41))) / sqrt(41).

(End)

Mathematica

CoefficientList[Series[(2+2x)/(1-8x-25x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, 25}, {2, 18}, 30] (* Harvey P. Dale, Sep 18 2021 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (2+2*x)/(1-8*x-25*x^2))); // Marius A. Burtea, Jan 13 2020
(Magma) a:=[2, 18]; [n le 2 select a[n] else 8*Self(n-1)+25 *Self(n-2):n in [1..25]]; // Marius A. Burtea, Jan 13 2020
(PARI) Vec(2*(1 + x) / (1 - 8*x - 25*x^2) + O(x^20)) \\ Colin Barker, Jan 13 2020

Crossrefs

Sequence in context: A066274 A052623 A362992 * A157765 A156341 A262718

Adjacent sequences: A155539 A155540 A155541 * A155543 A155544 A155545

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2010

Status

approved