A192742 Number of matchings in the n-antiprism graph.

3, 15, 51, 191, 708, 2631, 9775, 36319, 134943, 501380, 1862875, 6921503, 25716811, 95550687, 355018116, 1319068095, 4900991135, 18209608887, 67657713855, 251381908996, 934008268531, 3470303209839, 12893894812259, 47907203888767, 177998984624708, 661354367518327, 2457258957728079, 9129933787225743, 33922224882718431, 126037862684586116

Offset: 1

Author

Eric W. Weisstein, Jul 09 2011

Keywords

• nonn
• easy

Comments

Antiprism graphs have n >= 3; sequence extended via recurrence to start at n = 1

Links

• Eric Weisstein's World of Mathematics, Antiprism Graph
• Eric Weisstein's World of Mathematics, Independent Edge Set
• Eric Weisstein's World of Mathematics, Matching
• Index entries for linear recurrences with constant coefficients, signature (3,3,-1,-1).

Crossrefs

Bisection of A073817.

Programs

Mathematica

LinearRecurrence[{3, 3, -1, -1}, {3, 15, 51, 191}, 20]
Table[RootSum[1 + # - 3 #^2 - 3 #^3 + #^4 &, #^n &], {n, 20}]
CoefficientList[Series[(3 + 6 x - 3 x^2 - 4 x^3)/(1 - 3 x - 3 x^2 + x^3 + x^4), {x, 0, 20}], x]

Formula

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

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

a(n) = A073817(2*n). - Greg Dresden, Jan 27 2021