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
Index entries for linear recurrences with constant coefficients, signature (3,3,-1,-1).
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 09 2011
STATUS
approved