A292045 - OEIS

%I #8 Sep 08 2017 09:10:15

%S 0,48,972,7680,37500,136080,403368,1032192,2361960,4950000,9663060,

%T 17791488,31188612,52437840,85050000,133693440,204459408,305165232,

%U 445697820,638400000,898502220,1244602128,1699194552,2289254400,3046875000,4009964400,5223002148

%N Wiener index of the n X n X n grid graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid 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 (8,-28,56,-70,56,-28,8,-1).

%F a(n) = (n - 1)*(n + 1)*n^5/2.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

%F G.f.: 12*x^2*(4 + 49*x + 104*x^2 + 49*x^3 + 4*x^4)/(1 - x)^8.

%t Table[(n - 1) (n + 1) n^5/2, {n, 20}]

%t LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 48, 972, 7680, 37500, 136080, 403368, 1032192}, 20]

%t CoefficientList[Series[12 x (4 + 49 x + 104 x^2 + 49 x^3 + 4 x^4)/(1 - x)^8, {x, 0, 20}], x]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Sep 08 2017