A287425 Number of maximal matchings in the n-gear graph.

3, 6, 11, 22, 47, 98, 198, 394, 776, 1512, 2917, 5582, 10610, 20050, 37697, 70562, 131565, 244460, 452829, 836482, 1541318, 2833624, 5198692, 9519722, 17402027, 31759964, 57878498, 105331522, 191445503, 347548382, 630235055, 1141662370, 2066086475

Offset

1,1

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Gear Graph

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Maximal Independent Edge Set

Index entries for linear recurrences with constant coefficients, signature (5,-10,12,-11,7,-3,1).

Formula

G.f.: x*(3 - 9*x + 11*x^2 - 9*x^3 + 8*x^4 - 4*x^5 + 2*x^6) / ((1 - x)*(1 - 2*x + x^2 - x^3)^2)). - Colin Barker, May 25 2017

Mathematica

LinearRecurrence[{5, -10, 12, -11, 7, -3, 1}, {3, 6, 11, 22, 47, 98, 198}, 30]
CoefficientList[Series[(-3 + 9 x - 11 x^2 + 9 x^3 - 8 x^4 + 4 x^5 - 2 x^6)/((-1 + x) (-1 + 2 x - x^2 + x^3)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 30 2017 *)
Table[2 - n RootSum[-1 + # - 2 #^2 + #^3 &, 6 #^(n + 1) - 11 #^(n + 2) + 2 #^(n + 3) &]/23, {n, 20}] (* Eric W. Weisstein, Dec 30 2017 *)

Prog

(PARI) Vec(x*(3 - 9*x + 11*x^2 - 9*x^3 + 8*x^4 - 4*x^5 + 2*x^6) / ((1 - x)*(1 - 2*x + x^2 - x^3)^2) + O(x^40)) \\ Colin Barker, May 25 2017

Crossrefs

Sequence in context: A068033 A293337 A293364 * A088052 A045693 A051284

Adjacent sequences: A287422 A287423 A287424 * A287426 A287427 A287428

Keyword

nonn,easy

Author

Eric W. Weisstein, May 24 2017

Status

approved