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A296819
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Maximum detour index of any bipartite graph on n nodes.
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5
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0, 1, 4, 16, 32, 69, 108, 184, 256, 385, 500, 696, 864, 1141, 1372, 1744, 2048, 2529, 2916, 3520, 4000, 4741, 5324, 6216, 6912, 7969, 8788, 10024, 10976, 12405, 13500, 15136, 16384, 18241, 19652, 21744, 23328, 25669, 27436, 30040, 32000, 34881, 37044, 40216
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Bipartite Graph.
Eric Weisstein's World of Mathematics, Detour Index
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
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FORMULA
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a(2*n-1) = 4*(n-1)^3, a(2*n) = n*(4*n^2 - 5*n + 2).
a(n^2) = A296779(n), a(n^3) = A296780(n), a(n!) = A296785(n), a(2^n) = A288720(n).
From Colin Barker, Dec 21 2017: (Start)
G.f.: x^2*(1 + 3*x + 9*x^2 + 7*x^3 + 4*x^4) / ((1 - x)^4*(1 + x)^3).
a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.
(End)
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MATHEMATICA
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Rest@ CoefficientList[Series[x^2*(1 + 3 x + 9 x^2 + 7 x^3 + 4 x^4)/((1 - x)^4*(1 + x)^3), {x, 0, 44}], x] (* Michael De Vlieger, Dec 24 2017 *)
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PROG
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(PARI)
MaxBipartiteDetourIndex(a, b) = { a*(a-1)*min(a-1, b) + b*(b-1)*min(b-1, a) + a*b*(2*min(a, b)-1) }
a(n) = MaxBipartiteDetourIndex(floor(n/2), ceil(n/2));
(PARI) concat(0, Vec(x^2*(1 + 3*x + 9*x^2 + 7*x^3 + 4*x^4) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, Dec 21 2017
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CROSSREFS
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Cf. A288720, A296779, A296780, A296785.
Sequence in context: A119677 A326873 A126032 * A034713 A101653 A043100
Adjacent sequences: A296816 A296817 A296818 * A296820 A296821 A296822
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KEYWORD
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nonn,easy
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AUTHOR
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Andrew Howroyd, Dec 21 2017
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STATUS
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approved
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