A296197 Harary index of the n X n bishop graph.

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

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