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A228312 Triangle read by rows: T(m,n) (1<=n<=m) is the hyper-Wiener index of the complete bipartite graph K(m,n). 1
1, 5, 10, 12, 18, 27, 22, 29, 39, 52, 35, 43, 54, 68, 85, 51, 60, 72, 87, 105, 126, 70, 80, 93, 109, 128, 150, 175, 92, 103, 117, 134, 154, 177, 203, 232, 117, 129, 144, 162, 183, 207, 234, 264, 297, 145, 158, 174, 193, 215, 240, 268, 299, 333, 370, 176, 190, 207, 227, 250, 276, 305 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(n,n) = 4n^2 - 3n = A001107(n).

LINKS

Table of n, a(n) for n=1..62.

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

T(m,n) = (3(m+n)^2 - 4mn - 3m - 3n)/2.

The Hosoya-Wiener polynomial of K(m,n) is mnt + (1/2)(m^2 + n^2 - m - n) t^2.

G.f.: x*y*(1+2*x+2*y+3*x^2*y+3*y^2*x-11*x*y)/((1-x)^3*(1-y)^3). - R. J. Mathar, Nov 27 2015

EXAMPLE

Triangle begins:

    1,

    5, 10,

   12, 18, 27,

   22, 29, 39, 52,

   35, 43, 54, 68, 85,

   51, 60, 72, 87,105,126,

   70, 80, 93,109,128,150,175,

   92,103,117,134,154,177,203,232,

  117,129,144,162,183,207,234,264,297,

  145,158,174,193,215,240,268,299,333,370,

MAPLE

HWi := proc (m, n) options operator, arrow: (3/2)*(m+n)^2-2*m*n-(3/2)*m-(3/2)*n end proc: for m to 10 do seq(HWi(m, n), n = 1 .. m) end do; # yields sequence in triangular form

CROSSREFS

Cf. A001107, A182491.

Sequence in context: A313368 A313369 A101839 * A313370 A313371 A313372

Adjacent sequences:  A228309 A228310 A228311 * A228313 A228314 A228315

KEYWORD

nonn,tabl,easy

AUTHOR

Emeric Deutsch, Aug 25 2013

STATUS

approved

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Last modified September 29 18:39 EDT 2022. Contains 357090 sequences. (Running on oeis4.)