A296198 Harary index of the n X n black bishop graph.

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

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