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A157765
Expansion of (2 - 2*x) / (1 - 10*x - 7*x^2).
1
2, 18, 194, 2066, 22018, 234642, 2500546, 26647954, 283983362, 3026369298, 32251576514, 343700350226, 3662764537858, 39033547830162, 415974830066626, 4432983135477394, 47241655165240322, 503447433600744978, 5365165922164132034, 57175791256846535186
OFFSET
0,1
LINKS
Tomislav Došlić and Frode Måløy, Chain hexagonal cacti: Matchings and independent sets, Discr. Math., 310 (2010), 1676-1690.
FORMULA
From Colin Barker, Nov 25 2017: (Start)
a(n) = ((5-4*sqrt(2))^n*(-1+sqrt(2)) + (1+sqrt(2))*(5+4*sqrt(2))^n) / sqrt(2).
a(n) = 10*a(n-1) + 7*a(n-2) for n > 1.
(End)
MATHEMATICA
CoefficientList[Series[(2-2x)/(1-10x-7x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, 7}, {2, 18}, 30] (* Harvey P. Dale, Feb 25 2020 *)
PROG
(PARI) Vec(2*(1 - x) / (1 - 10*x - 7*x^2) + O(x^40)) \\ Colin Barker, Nov 25 2017
CROSSREFS
Sequence in context: A052623 A362992 A155542 * A156341 A262718 A210989
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 22 2010
STATUS
approved