The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A143368 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A143368

Triangle read by rows: T(n,k) is the Wiener index of a k X n grid (i.e., P_k X P_n, where P_m is the path graph on m vertices; 1 <= k <= n).
(history; published version)

#30 by Jon E. Schoenfield at Fri Jul 21 17:34:01 EDT 2017

STATUS

editing

approved

#29 by Jon E. Schoenfield at Fri Jul 21 17:33:58 EDT 2017

NAME

Triangle read by rows: T(n,k) is the Wiener index of a k x X n grid, (i.e. , P_k x X P_n, where P_m is the path graph on m vertices; 1 <= k <= n).

FORMULA

T(n,k) = k*n*(n+k)*(k*n-1)/6 (k, n >= 1).

EXAMPLE

T(3,2)=25 because on the P(2)xP X P(3) graph there are 7 distances equal to 1, 6 distances equal to 2 and 2 distances equal to 3, with 7*1 + 6*2 + 2*3 = 25.

STATUS

approved

editing

#28 by N. J. A. Sloane at Sun May 28 09:21:43 EDT 2017

STATUS

proposed

approved

#27 by Michel Marcus at Sun May 28 08:41:36 EDT 2017

STATUS

editing

proposed

#26 by Michel Marcus at Sun May 28 08:41:31 EDT 2017

CROSSREFS

Cf. A180569 (row 3), A131423 (row 2).

STATUS

proposed

editing

#25 by Michel Marcus at Sun May 28 08:41:09 EDT 2017

STATUS

editing

proposed

#24 by Michel Marcus at Sun May 28 08:41:03 EDT 2017

REFERENCES

B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60 (1996), 959-969, doi:10.1002/(SICI)1097-461X(1996)60:5<959::AID-QUA2>3.0.CO;2-W

LINKS

B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://dx.doi.org/10.1002/(SICI)1097-461X(1996)60:5<959::AID-QUA2>3.0.CO;2-W">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.

FORMULA

T(n,k) =kn k*n*(n+k)*(knk*n-1)/6 (k,n>=1).

STATUS

proposed

editing

#23 by Michael De Vlieger at Sun May 28 08:26:07 EDT 2017

STATUS

editing

proposed

#22 by Michael De Vlieger at Sun May 28 08:25:57 EDT 2017

LINKS

Michael De Vlieger, <a href="/A143368/b143368.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150).

#21 by Michael De Vlieger at Sun May 28 08:24:02 EDT 2017

MATHEMATICA

Table[k n (n + k) (k n - 1)/6, {n, 9}, {k, n}] // Flatten (* Michael De Vlieger, May 28 2017 *)

STATUS

reviewed

editing