cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A228316 The hyper-Wiener index of the Cartesian product of the cycles C(n) and C(n) (a Torus Grid Graph).

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%I A228316 #13 Mar 29 2020 13:07:42
%S A228316 0,10,72,448,1450,4482,10388,23552,45360,86250,147620,250560,395122,
%T A228316 619458,919800,1359872,1928208,2725002,3725520,5080000,6742890,
%U A228316 8931010,11568172,14957568,18980000,24048362,29985228,37340352,45859730,56261250
%N A228316 The hyper-Wiener index of the Cartesian product of the cycles C(n) and C(n) (a Torus Grid Graph).
%C A228316 a(n) = A228314(n,n).
%H A228316 B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://users.math.msu.edu/users/sagan/Papers/Old/wpg-pub.pdf">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.
%F A228316 a(n) = n^2*(n^2-1)*(7*n^2+12*n-3)/96 if n is odd; a(n) = n^4*(7*n^2+12*n+8)/96 if n is even.
%F A228316 G.f.: 2*x^2*(5 + 26*x + 132*x^2 + 183*x^3 +280*x^4 + 132*x^5 +74*x^6 + 7*x^7 + x^8) / ((1-x)^7*(1+x)^5).
%p A228316 a := proc (n) if `mod`(n, 2) = 1 then (1/96)*n^2*(n^2-1)*(7*n^2+12*n-3) else (1/96)*n^4*(7*n^2+12*n+8) end if end proc: seq(a(n), n = 1 .. 30);
%Y A228316 Cf. A228314, A122657.
%K A228316 nonn,easy
%O A228316 1,2
%A A228316 _Emeric Deutsch_, Aug 26 2013