A292059 - OEIS

%I #4 Sep 08 2017 13:36:21

%S 1,8,42,104,251,464,852,1360,2165,3160,4606,6328,8687,11424,15016,

%T 19104,24297,30120,37330,45320,55011,65648,78332,92144,108381,125944,

%U 146342,168280,193495,220480,251216,283968,320977,360264,404346,450984,502987,557840,618660,682640

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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WienerIndex.html">Wiener Index</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) = (3 + 2*n - 6*n^2 - 8*n^3 + 6*n^4 + 3*(-1)^n*(-1 - 2*n + 2*n^2))/24.

%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 - 6*x - 24*x^2 - 10*x^3 - 7 x^4)/((-1 + x)^5*(1 + x)^3).

%t Table[(3 + 2 n - 6 n^2 - 8 n^3 + 6 n^4 + 3 (-1)^n (-1 - 2 n + 2 n^2))/24, {n, 2, 20}]

%t LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 8, 42, 104, 251, 464, 852, 1360}, 20]

%t CoefficientList[Series[(-1 - 6 x - 24 x^2 - 10 x^3 - 7 x^4)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

%K nonn,easy

%O 2,2

%A _Eric W. Weisstein_, Sep 08 2017