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A290779
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Number of 6-cycles in the n-triangular honeycomb bishop graph.
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3
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0, 0, 1, 57, 486, 2360, 8394, 24354, 61104, 137412, 283635, 546403, 994422, 1725516, 2875028, 4625700, 7219152, 10969080, 16276293, 23645709, 33705430, 47228016, 65154078, 88618310, 118978080, 157844700, 207117495, 269020791, 346143942, 441484516, 558494760
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OFFSET
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1,4
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LINKS
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Table of n, a(n) for n=1..31.
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
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FORMULA
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a(n) = binomial(n + 1, 4)*(-62 + 11*n - 109*n^2 + 40*n^3)/70.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
G.f.: (x (x^2 + 49 x^3 + 58 x^4 + 12 x^5))/(-1 + x)^8.
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MATHEMATICA
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Table[Binomial[n + 1, 4] (-62 + 11 n - 109 n^2 + 40 n^3)/70, {n, 20}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 1, 57, 486, 2360, 8394, 24354}, 40]
CoefficientList[Series[(x^2 + 49 x^3 + 58 x^4 + 12 x^5)/(-1 + x)^8, {x, 0, 20}], x]
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PROG
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(PARI) a(n)=n*(40*n^6 - 189*n^5 + 189*n^4 + 105*n^3 - 105*n^2 + 84*n - 124)/1680 \\ Charles R Greathouse IV, Aug 10 2017
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CROSSREFS
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Cf. A034827 (3-cycles), A051843 (4-cycles), A290775 (5-cycles).
Sequence in context: A184224 A337629 A218812 * A027143 A164786 A240416
Adjacent sequences: A290776 A290777 A290778 * A290780 A290781 A290782
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Aug 10 2017
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STATUS
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approved
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