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A290392
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Number of 6-cycles in the n-triangular honeycomb obtuse knight graph.
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3
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0, 0, 0, 0, 4, 13, 98, 415, 1151, 2471, 4385, 6893, 9995, 13691, 17981, 22865, 28343, 34415, 41081, 48341, 56195, 64643, 73685, 83321, 93551, 104375, 115793, 127805, 140411, 153611, 167405, 181793, 196775, 212351, 228521, 245285, 262643, 280595
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OFFSET
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1,5
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LINKS
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FORMULA
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For n >= 9, a(n) = 16001 - 4323*n + 297*n^2.
For n >= 12, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: x^5*(-4 - x - 71*x^2 - 156*x^3 - 187*x^4 - 165*x^5 - 10*x^6)/(-1 +
x)^3.
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MATHEMATICA
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Table[Piecewise[{{0, n <= 4}, {4, n == 5}, {13, n == 6}, {98, n == 7}, {415, n == 8}, {16001 - 4323 n + 297 n^2, n > 8}}, 0], {n, 20}]
Join[{0, 0, 0, 0, 4, 13, 98, 415}, LinearRecurrence[{3, -3, 1}, {1151, 2471, 4385}, 12]]
CoefficientList[Series[(x^4 (-4 - x - 71 x^2 - 156 x^3 - 187 x^4 - 165 x^5 - 10 x^6))/(-1 + x)^3, {x, 0, 20}], x]
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CROSSREFS
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Cf. A001105 (3-cycles in the triangular honeycomb obtuse knight graph), A194715 (4-cycles), A290391 (5-cycles).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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