A293126 Number of matchings in the 2n-crossed prism graph.

3, 12, 108, 1092, 11208, 115272, 1185888, 12200592, 125522208, 1291399392, 13286195328, 136691243712, 1406309006208, 14468410468992, 148854128491008, 1531443389475072, 15755820002738688, 162099275536276992, 1667712319943927808, 17157784159685102592

Offset

0,1

Comments

Extended to a(0)-a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Eric Weisstein's World of Mathematics, Independent Vertex Set

Eric Weisstein's World of Mathematics, Vertex Cover

Index entries for linear recurrences with constant coefficients, signature (12, -18, 4).

Formula

a(n) = 12*a(n-1) - 18*a(n-2) + 4*a(n-3).

G.f.: -3*x*(1 - 8*x + 6*x^2)/(-1 + 12*x - 18*x^2 + 4*x^3).

Mathematica

RootSum[-4 + 18 # - 12 #^2 + #^3 &, #^Range[0, 20] &]
Table[RootSum[-4 + 18 # - 12 #^2 + #^3 &, #^n &], {n, 0, 20}]
LinearRecurrence[{12, -18, 4}, {12, 108, 1092}, {0, 20}]
CoefficientList[Series[-3 (1 - 8 x + 6 x^2)/(-1 + 12 x - 18 x^2 + 4 x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A141535 A324313 A111485 * A080447 A127059 A178013

Adjacent sequences: A293123 A293124 A293125 * A293127 A293128 A293129

Keyword

nonn

Author

Eric W. Weisstein, Sep 30 2017

Status

approved