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A129033
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Number of n-node triangulations of the torus S_1 in which every node has degree >= 6.
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0
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0, 1, 1, 2, 1, 1, 4, 2, 2, 4, 5, 2, 5, 3, 6, 6, 4, 3, 11, 5, 5, 7, 9, 4, 11, 5, 11, 8, 7, 8, 16, 6, 8, 10, 16, 6, 15, 7, 13, 14, 10, 7, 24, 10, 14, 12, 16, 8, 19, 12, 21, 14, 13, 9, 30, 10, 14, 19, 23, 14, 23, 11, 20, 16, 23, 11, 36, 12, 17, 22, 23, 16, 27, 13, 34, 21, 19, 13, 40, 18, 20, 20, 31, 14, 39, 20, 27, 22, 22, 20, 47, 16, 27, 27, 37
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OFFSET
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6,4
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LINKS
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MATHEMATICA
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T2[n_] := Piecewise[{{DivisorSigma[0, n] - 2 - T6[n], Mod[n, 2] == 1}, {DivisorSigma[0, n/2] - 2, Mod[n, 4] == 2}}, DivisorSigma[0, n/2] + DivisorSigma[0, n/4] - 4 - T6[n]];
T3[n_] := Length[{ToRules[Reduce[n == p^2 + p q + q^2 && 0 < q < p, {p, q}, Integers]]}];
T6[n_] := Boole[n >= 9 && (IntegerQ[Sqrt[n]] || IntegerQ[Sqrt[n/3]])]
T[n_] := Piecewise[{{DivisorSigma[1, n]/6 + T2[n]/2 + 2/3 T3[n] +
5/6 T6[n] - (2 - Mod[n, 2]), n > 6}}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Terms a(18) and beyond from Thom Sulanke added by Ed Pegg Jr, Aug 30 2018
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STATUS
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approved
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