A296819 Maximum detour index of any bipartite graph on n nodes.

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

Offset

1,3

Links

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).

Formula

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)

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A288720, A296779, A296780, A296785.

Sequence in context: A119677 A326873 A126032 * A034713 A101653 A043100

Adjacent sequences: A296816 A296817 A296818 * A296820 A296821 A296822

Keyword

nonn,easy

Author

Andrew Howroyd, Dec 21 2017

Status

approved