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

1,2

Comments

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

Links

Table of n, a(n) for n=1..30.

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

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).

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);

Crossrefs

Cf. A228314, A122657.

Sequence in context: A271035 A108276 A264159 * A228310 A164546 A221552

Adjacent sequences: A228313 A228314 A228315 * A228317 A228318 A228319

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 26 2013

Status

approved