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A228316 The hyper-Wiener index of the Cartesian product of the cycles C(n) and C(n) (a Torus Grid Graph). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)