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A296198 Harary index of the n X n black bishop graph. 0
0, 1, 8, 21, 55, 104, 197, 318, 514, 755, 1110, 1531, 2113, 2786, 3675, 4684, 5972, 7413, 9204, 11185, 13595, 16236, 19393, 22826, 26870, 31239, 36322, 41783, 48069, 54790, 62455, 70616, 79848, 89641, 100640, 112269, 125247, 138928, 154109, 170070 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Eric Weisstein's World of Mathematics, Black Bishop Graph

Eric Weisstein's World of Mathematics, Harary Index

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

FORMULA

a(n) = (-15 + 20*n - 30*n^2 + 16*n^3 + 6*n^4 - 3*(-1)^n*(2*n^2 + 4*n - 5))/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 - 6*x - 3*x^2 - 3*x^3 + x^5)/((-1 + x)^5*(1 + x)^3).

MATHEMATICA

Table[(-15 + 20 n - 30 n^2 + 16 n^3 + 6 n^4 - 3 (-1)^n (2 n^2 + 4 n - 5))/96, {n, 20}]

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 1, 8, 21, 55, 104, 197, 318}, 20]

CoefficientList[Series[x (-1 - 6 x - 3 x^2 - 3 x^3 + x^5)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

PROG

(PARI) first(n) = Vec(x^2*(-1 - 6*x - 3*x^2 - 3*x^3 + x^5)/((-1 + x)^5*(1 + x)^3) + O(x^(n+1)), -n) \\ Iain Fox, Dec 07 2017

CROSSREFS

Sequence in context: A067334 A066859 A227653 * A301538 A192299 A080144

Adjacent sequences:  A296195 A296196 A296197 * A296199 A296200 A296201

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Dec 07 2017

STATUS

approved

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Last modified October 20 10:21 EDT 2021. Contains 348100 sequences. (Running on oeis4.)