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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 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.)