A364370 Number of chordless cycles (of length > 3) in the complement of the n-hypercube graph.

0, 0, 0, 6, 160, 1720, 13056, 82656, 470016, 2496384, 12666880, 62250496, 298868736, 1409660928, 6556483584, 30148976640, 137316794368, 620328091648, 2782435737600, 12402204475392, 54971691171840, 242433274675200, 1064306401607680, 4653085408362496

Offset

0,4

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Chordless Cycle.

Eric Weisstein's World of Mathematics, Hypercube Graph.

Index entries for linear recurrences with constant coefficients, signature (20,-168,768,-2064,3264,-2816,1024).

Formula

a(n) = 2^(n - 2)*n*Sum_{j=0..n-3} Sum_{k=3..n-j} 4*((k + 2)*2^(k - 5) - 1). - Detlef Meya, Jun 23 2024

G.f.: 2*x^3*(3 + 20*x - 236*x^2 + 464*x^3)/((1 - 2*x)^4*(1 - 4*x)^3). - Andrew Howroyd, Nov 14 2025

a(n) = 20*a(n-1) - 168*a(n-2) + 768*a(n-3) - 2064*a(n-4) + 3264*a(n-5) - 2816*a(n-6) + 1024*a(n-7). - Wesley Ivan Hurt, Jun 05 2026

Mathematica

a[n_] := 2^(n - 2)*n*Sum[Sum[4*((k + 2)*2^(k - 5) - 1), {k, 3, n-j}], {j, 0, n-3}]; Table[a[n], {n, 0, 21}] (* Detlef Meya, Jun 23 2024 *)

Crossrefs

Cf. A361149.

Sequence in context: A324231 A283728 A030449 * A120277 A241453 A381757

Adjacent sequences: A364367 A364368 A364369 * A364371 A364372 A364373

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 20 2023

Extensions

a(10) from Pontus von Brömssen, Jul 28 2023

a(11) and beyond from Detlef Meya, Jun 23 2024

Status

approved