A157765 Expansion of (2 - 2*x) / (1 - 10*x - 7*x^2).

2, 18, 194, 2066, 22018, 234642, 2500546, 26647954, 283983362, 3026369298, 32251576514, 343700350226, 3662764537858, 39033547830162, 415974830066626, 4432983135477394, 47241655165240322, 503447433600744978, 5365165922164132034, 57175791256846535186

Offset

0,1

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 (10, 7).

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

Adjacent sequences: A157762 A157763 A157764 * A157766 A157767 A157768

Keyword

nonn,easy

Author

N. J. A. Sloane, May 22 2010

Status

approved