A296196 Harary index of the n X n queen graph.

0, 6, 32, 98, 230, 460, 826, 1372, 2148, 3210, 4620, 6446, 8762, 11648, 15190, 19480, 24616, 30702, 37848, 46170, 55790, 66836, 79442, 93748, 109900, 128050, 148356, 170982, 196098, 223880, 254510, 288176, 325072, 365398, 409360, 457170, 509046, 565212, 625898, 691340

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Harary Index

Eric Weisstein's World of Mathematics, Queen Graph

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = n*(n - 1)*(3*n^2 + 13*n - 2)/12.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: 2*x^2*(-3 - x + x^2)/(-1 + x)^5.

Mathematica

Table[n (n - 1) (3 n^2 + 13 n - 2)/12, {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 6, 32, 98, 230}, 40]
CoefficientList[Series[2 x (-3 - x + x^2)/(-1 + x)^5, {x, 0, 20}], x]

Prog

(PARI) first(n) = Vec(2*x^2*(-3 - x + x^2)/(-1 + x)^5 + O(x^(n+1)), -n) \\ Iain Fox, Dec 07 2017

Crossrefs

Sequence in context: A161844 A305291 A177082 * A211918 A288961 A090382

Adjacent sequences: A296193 A296194 A296195 * A296197 A296198 A296199

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2017

Status

approved