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A290026 Number of 3-cycles in the n-halved cube graph. 3
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 (list; graph; refs; listen; history; text; internal format)
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

AUTHOR

Eric W. Weisstein, Jul 17 2017

STATUS

approved

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Last modified June 25 10:09 EDT 2021. Contains 345453 sequences. (Running on oeis4.)