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A155049
Expansion of (1+5*x)/(1-13*x+10*x^2).
1
1, 18, 224, 2732, 33276, 405268, 4935724, 60111732, 732095276, 8916121268, 108588623724, 1322490895732, 16106495407276, 196159531337268, 2389008953311724, 29095521079679732, 354351684502719276, 4315616687738553268, 52559500095573999724, 640117334365076463732
OFFSET
0,2
LINKS
Tomislav Došlić and Frode Måløy, Chain hexagonal cacti: Matchings and independent sets, Discr. Math., 310 (2010), 1676-1690.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 22 2010
STATUS
approved