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A296200 Harary index of the n X n white bishop graph. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)