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

0, 10, 72, 448, 1450, 4482, 10388, 23552, 45360, 86250, 147620, 250560, 395122, 619458, 919800, 1359872, 1928208, 2725002, 3725520, 5080000, 6742890, 8931010, 11568172, 14957568, 18980000, 24048362, 29985228, 37340352, 45859730, 56261250

Offset: 1

Author

Emeric Deutsch, Aug 26 2013

Keywords

• nonn
• easy

Comments

a(n) = A228314(n,n).

Links

• B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.

Crossrefs

Cf. A228314, A122657.

Programs

Maple

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);

Formula

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.

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).