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A296197 Harary index of the n X n bishop graph. 0
0, 2, 13, 42, 102, 208, 379, 636, 1004, 1510, 2185, 3062, 4178, 5572, 7287, 9368, 11864, 14826, 18309, 22370, 27070, 32472, 38643, 45652, 53572, 62478, 72449, 83566, 95914, 109580, 124655, 141232, 159408, 179282, 200957, 224538, 250134, 277856, 307819, 340140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Eric Weisstein's World of Mathematics, Bishop Graph

Eric Weisstein's World of Mathematics, Harary Index

Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4, 1).

FORMULA

a(n) = (3 + 8*n - 36*n^2 + 16*n^3 + 6*n^4 - 3 (-1)^n)/48.

a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).

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

MATHEMATICA

Table[(3 + 8 n - 36 n^2 + 16 n^3 + 6 n^4 - 3 (-1)^n)/48, {n, 10}]

LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 2, 13, 42, 102, 208}, 40]

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

PROG

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

CROSSREFS

Sequence in context: A219054 A154354 A138089 * A026594 A240173 A235469

Adjacent sequences:  A296194 A296195 A296196 * A296198 A296199 A296200

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Dec 07 2017

STATUS

approved

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Last modified February 27 03:50 EST 2020. Contains 332299 sequences. (Running on oeis4.)