A296200 Harary index of the n X n white bishop graph.

1, 5, 21, 47, 104, 182, 318, 490, 755, 1075, 1531, 2065, 2786, 3612, 4684, 5892, 7413, 9105, 11185, 13475, 16236, 19250, 22826, 26702, 31239, 36127, 41783, 47845, 54790, 62200, 70616, 79560, 89641, 100317, 112269, 124887, 138928, 153710, 170070, 187250

Offset

2,2

Links

Table of n, a(n) for n=2..41.

Eric Weisstein's World of Mathematics, Harary Index

Eric Weisstein's World of Mathematics, White Bishop Graph

Index entries for linear recurrences with constant coefficients, signature (2, 2, -6, 0, 6, -2, -2, 1).

Formula

a(n) = (21 - 4*n - 42*n^2 + 16*n^3 + 6*n^4 + 3*(-1)^n*(-7 + 4*n + 2*n^2))/96.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

G.f.: x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3).

Mathematica

Table[(21 - 4 n - 42 n^2 + 16 n^3 + 6 n^4 + 3 (-1)^n (-7 + 4 n + 2 n^2))/96, {n, 20}]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 5, 21, 47, 104, 182, 318, 490}, 20]
CoefficientList[Series[(-1 - 3 x - 9 x^2 - x^3 + 2 x^4)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

Prog

(PARI) first(n) = Vec(x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3) + O(x^(n+2))) \\ Iain Fox, Dec 07 2017

Crossrefs

Sequence in context: A049741 A166010 A146846 * A041825 A022268 A201279

Adjacent sequences: A296197 A296198 A296199 * A296201 A296202 A296203

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2017

Status

approved