A290026 Number of 3-cycles in the n-halved cube graph.

0, 0, 4, 32, 160, 640, 2240, 7168, 21504, 61440, 168960, 450560, 1171456, 2981888, 7454720, 18350080, 44564480, 106954752, 254017536, 597688320, 1394606080, 3229614080, 7428112384, 16978542592, 38587596800, 87241523200, 196293427200, 439697276928, 980863156224

Offset

1,3

Comments

a(n) is the number of diagonals of length sqrt(3) in an n-cube. - Nigel Stepp, Oct 06 2019

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Halved Cube 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-3)-16*a(n-4).

G.f.: (4*x^3)/(-1 + 2*x)^4.

Mathematica

Table[2^(n - 1) Binomial[n, 3], {n, 20}]
LinearRecurrence[{8, -24, 32, -16}, {0, 0, 4, 32}, 20]
CoefficientList[Series[(4 x^2)/(-1 + 2 x)^4, {x, 0, 20}], x]

Crossrefs

Cf. A290027 (4-cycles), A290028 (5-cycles), A290029 (6-cycles).

Sequence in context: A270161 A270977 A270287 * A272511 A271415 A270619

Adjacent sequences: A290023 A290024 A290025 * A290027 A290028 A290029

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Jul 17 2017

Status

approved