Voozh

A285186

Expansion of (x+2*x^2) / (1-2*x-2*x^2+2*x^3).

0, 1, 4, 10, 26, 64, 160, 396, 984, 2440, 6056, 15024, 37280, 92496, 229504, 569440, 1412896, 3505664, 8698240, 21582016, 53549184, 132865920, 329666176, 817965824, 2029532160, 5035663616, 12494459904, 31001182720, 76919958016, 190853361664, 473544273920, 1174955355136, 2915292534784

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276. See Prop. 4.11.

Index entries for linear recurrences with constant coefficients, signature (2,2,-2).

FORMULA

a(n) = A285185(n)/2.

a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) for n>2. - Colin Barker, Apr 23 2017

PROG

(PARI) concat(0, Vec(x*(1 + 2*x) / (1 - 2*x - 2*x^2 + 2*x^3) + O(x^30))) \\ Colin Barker, Apr 23 2017