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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 22 2010
STATUS
approved