A292054 Wiener index of the n X n knight graph.

288, 708, 1580, 3144, 5804, 9996, 16388, 25660, 38808, 56808, 81048, 112856, 154080, 206448, 272332, 353920, 454172, 575784, 722372, 897196, 1104592, 1348436, 1633848, 1965376, 2348992, 2789964, 3295180, 3870688, 4524356, 5263060, 6095716, 7030084, 8076192

Offset

4,1

Comments

The square knight graph is connected for n >= 4.

Links

Colin Barker, Table of n, a(n) for n = 4..1000

Eric Weisstein's World of Mathematics, Knight Graph

Eric Weisstein's World of Mathematics, Wiener Index

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,-1,2,2,-1,0,-3,1,2,-1).

Formula

a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-5) + 2*a(n-6) + 2*a(n-7) - a(n-8) - 3*a(n-10) + a(n-11) + 2*a(n-12) - a(n-13) for n > 17.

G.f.: 4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 18 2017

Mathematica

Join[{288}, LinearRecurrence[{2, 1, -3, 0, -1, 2, 2, -1, 0, -3, 1, 2, -1}, {708, 1580, 3144, 5804, 9996, 16388, 25660, 38808, 56808, 81048, 112856, 154080, 206448}, 20]]

Prog

(PARI) Vec(4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)) + O(x^50)) \\ Colin Barker, Sep 18 2017

Crossrefs

Sequence in context: A082994 A127350 A158253 * A250788 A179646 A281236

Adjacent sequences: A292051 A292052 A292053 * A292055 A292056 A292057

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved