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%I #14 Mar 30 2020 04:18:31
%S 1,5,10,12,18,27,22,29,39,52,35,43,54,68,85,51,60,72,87,105,126,70,80,
%T 93,109,128,150,175,92,103,117,134,154,177,203,232,117,129,144,162,
%U 183,207,234,264,297,145,158,174,193,215,240,268,299,333,370,176,190,207,227,250,276,305
%N Triangle read by rows: T(m,n) (1<=n<=m) is the hyper-Wiener index of the complete bipartite graph K(m,n).
%C T(n,n) = 4n^2 - 3n = A001107(n).
%H B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://users.math.msu.edu/users/sagan/Papers/Old/wpg-pub.pdf">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.
%F T(m,n) = (3(m+n)^2 - 4mn - 3m - 3n)/2.
%F The Hosoya-Wiener polynomial of K(m,n) is mnt + (1/2)(m^2 + n^2 - m - n) t^2.
%F 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
%e Triangle begins:
%e 1,
%e 5, 10,
%e 12, 18, 27,
%e 22, 29, 39, 52,
%e 35, 43, 54, 68, 85,
%e 51, 60, 72, 87,105,126,
%e 70, 80, 93,109,128,150,175,
%e 92,103,117,134,154,177,203,232,
%e 117,129,144,162,183,207,234,264,297,
%e 145,158,174,193,215,240,268,299,333,370,
%p 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
%Y Cf. A001107, A182491.
%K nonn,tabl,easy
%O 1,2
%A _Emeric Deutsch_, Aug 25 2013
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