OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle.
Eric Weisstein's World of Mathematics, Hypercube Graph.
Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
FORMULA
a(n) = 2^(n + 1)*binomial(n, 3).
a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-4)-16*a(n-4).
G.f.: (16*x^3)/(-1 + 2*x)^4.
From Amiram Eldar, Jan 05 2022: (Start)
Sum_{n>=3} 1/a(n) = 3*(2*log(2)-1)/16.
Sum_{n>=3} (-1)^(n+1)/a(n) = (3/2)^3*log(3/2) - 21/16. (End)
MATHEMATICA
Table[2^(n + 1) Binomial[n, 3], {n, 0, 20}]
LinearRecurrence[{8, -24, 32, -16}, {0, 0, 0, 16}, 20]
CoefficientList[Series[(16 x^3)/(-1 + 2 x)^4, {x, 0, 20}], x]
Table[Length[FindCycle[HypercubeGraph[n], {6}, All]], {n, 0, 10}] (* Eric W. Weisstein, Aug 02 2023 *)
PROG
(Magma) [2^(n + 1)*Binomial(n, 3): n in [0..30]]; // Wesley Ivan Hurt, Apr 21 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 17 2017
STATUS
approved