OFFSET
2,3
COMMENTS
a(5) is also the number of 6-cycles in the 2-Keller graph.
LINKS
Eric Weisstein's World of Mathematics, Folded Cube Graph
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Keller Graph
Index entries for linear recurrences with constant coefficients, signature (8, -24, 32, -16).
FORMULA
a(n) = 2^(n - 1)*n*(n - 1)*(n - 2)/3 for n > 6.
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 10.
G.f.: 32*x^4*(3 - 14*x + 92*x^2 - 516*x^3 + 1456*x^4 - 1920*x^5 + 960*x^6)/(-1 + 2*x)^4.
MATHEMATICA
Table[Piecewise[{{0, n == 3}, {96, n == 4}, {3200, n == 6}}, 2^(n - 1) n (n - 1) (n - 2)/3], {n, 2, 20}]
Join[{0, 0, 96, 320, 3200}, LinearRecurrence[{8, -24, 32, -16}, {4480, 14336, 43008, 122880, 337920}, 14]]
CoefficientList[Series[32 x^2 (3 - 14 x + 92 x^2 - 516 x^3 + 1456 x^4 - 1920 x^5 + 960 x^6)/(-1 + 2 x)^4, {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 21 2018
STATUS
approved