A292051 Wiener index of the n X n black bishop graph.

0, 1, 14, 42, 124, 251, 506, 852, 1432, 2165, 3270, 4606, 6484, 8687, 11634, 15016, 19376, 24297, 30462, 37330, 45740, 55011, 66154, 78332, 92744, 108381, 126646, 146342, 169092, 193495, 221410, 251216, 285024, 320977, 361454, 404346, 452316, 502987, 559322, 618660

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, Wiener Index

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

Formula

a(n) = (3 - 10*n + 6*n^2 - 8*n^3 + 6*n^4 - 3*(-1)^n*(1 - 2*n + 2*n^2))/24.

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 - 12*x - 12*x^2 - 18*x^3 - 3*x^4 - 2*x^5)/((-1 + x)^5*(1 + x)^3).

Mathematica

Table[(3 - 10 n + 6 n^2 - 8 n^3 + 6 n^4 - 3 (-1)^n (1 - 2 n + 2 n^2))/24, {n, 20}]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 1, 14, 42, 124, 251, 506, 852}, 20]
CoefficientList[Series[x (-1 - 12 x - 12 x^2 - 18 x^3 - 3 x^4 - 2 x^5)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A005587 A244101 A212514 * A242897 A120714 A041378

Adjacent sequences: A292048 A292049 A292050 * A292052 A292053 A292054

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved