%I #6 Dec 07 2017 22:15:15

%S 1,5,21,47,104,182,318,490,755,1075,1531,2065,2786,3612,4684,5892,

%T 7413,9105,11185,13475,16236,19250,22826,26702,31239,36127,41783,

%U 47845,54790,62200,70616,79560,89641,100317,112269,124887,138928,153710,170070,187250

%N Harary index of the n X n white bishop graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, -6, 0, 6, -2, -2, 1).

%F a(n) = (21 - 4*n - 42*n^2 + 16*n^3 + 6*n^4 + 3*(-1)^n*(-7 + 4*n + 2*n^2))/96.

%F 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).

%F G.f.: x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3).

%t Table[(21 - 4 n - 42 n^2 + 16 n^3 + 6 n^4 + 3 (-1)^n (-7 + 4 n + 2 n^2))/96, {n, 20}]

%t LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 5, 21, 47, 104, 182, 318, 490}, 20]

%t CoefficientList[Series[(-1 - 3 x - 9 x^2 - x^3 + 2 x^4)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

%o (PARI) first(n) = Vec(x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3) + O(x^(n+2))) \\ _Iain Fox_, Dec 07 2017

%K nonn,easy

%O 2,2

%A _Eric W. Weisstein_, Dec 07 2017