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A290391
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Number of 5-cycles in the n-triangular honeycomb obtuse knight graph.
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3
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0, 0, 0, 0, 0, 0, 30, 120, 294, 552, 894, 1320, 1830, 2424, 3102, 3864, 4710, 5640, 6654, 7752, 8934, 10200, 11550, 12984, 14502, 16104, 17790, 19560, 21414, 23352, 25374, 27480, 29670, 31944, 34302, 36744, 39270, 41880, 44574, 47352, 50214, 53160, 56190, 59304, 62502
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OFFSET
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1,7
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LINKS
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FORMULA
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For n >= 7, a(n) = 6*(292 - 90*n + 7*n^2).
For n >= 10, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -6*x^7*(5 + 5*x + 4*x^2)/(-1 + x)^3.
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MATHEMATICA
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Table[If[n < 7, 0, 6 (292 - 90 n + 7 n^2)], {n, 20}]
Join[{0, 0, 0, 0, 0, 0}, LinearRecurrence[{3, -3, 1}, {30, 120, 294}, 14]]
CoefficientList[Series[-((6 x^6 (5 + 5 x + 4 x^2))/(-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), A290392 (6-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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