Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #6 Dec 07 2017 22:14:53
%S 0,2,13,42,102,208,379,636,1004,1510,2185,3062,4178,5572,7287,9368,
%T 11864,14826,18309,22370,27070,32472,38643,45652,53572,62478,72449,
%U 83566,95914,109580,124655,141232,159408,179282,200957,224538,250134,277856,307819,340140
%N Harary index of the n X n bishop graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BishopGraph.html">Bishop Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 0, 5, -4, 1).
%F a(n) = (3 + 8*n - 36*n^2 + 16*n^3 + 6*n^4 - 3 (-1)^n)/48.
%F a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6).
%F G.f.: x^2*(-2 - 5*x + x^3)/((-1 + x)^5 (1 + x)).
%t Table[(3 + 8 n - 36 n^2 + 16 n^3 + 6 n^4 - 3 (-1)^n)/48, {n, 10}]
%t LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 2, 13, 42, 102, 208}, 40]
%t CoefficientList[Series[x (-2 - 5 x + x^3)/((-1 + x)^5 (1 + x)), {x, 0, 20}], x]
%o (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
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Dec 07 2017