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A192742
Number of matchings in the n-antiprism graph.
4
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
1,1
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
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
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]
CROSSREFS
Bisection of A073817.
Sequence in context: A282464 A284663 A231747 * A166035 A038192 A212869
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 09 2011
STATUS
approved