# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a245826
Showing 1-1 of 1

%I A245826 #18 Feb 09 2018 11:10:41
%S A245826 0,1,16,4,59,216,10,144,526,1280,20,285,1040,2530,5000,35,496,1809,
%T A245826 4400,8695,15120,56,791,2884,7014,13860,24101,38416,84,1184,4316,
%U A245826 10496,20740,36064,57484,86016,120,1689,6156,14970,29580,51435,81984,122676,174960,165,2320,8455,20560,40625,70640,112595,168480,240285,330000
%N A245826 Triangle read by rows: T(m,n) is the Szeged index of the grid graph P_m X P_n  (1 <= n <= m).
%C A245826 T(n,1) = Szeged index of the path tree P_n = A000292(n-1).
%C A245826 T(n,2) = Szeged index of the ladder graph P_2 X P_n = A063521(n).
%C A245826 T(n,3) = Szeged index of the grid graph P_3 X P_n = A245827(n).
%C A245826 T(n,n) = Szeged index of the grid graph P_n X P_n = A245828(n).
%H A245826 Reinhard Zumkeller, <a href="/A245826/b245826.txt">Rows n = 1..125 of triangle, flattened</a>
%H A245826 S. Klavzar, A. Rajapakse, I. Gutman, <a href="http://dx.doi.org/10.1016/0893-9659(96)00071-7">The Szeged and the Wiener index of graphs</a>, Appl. Math. Lett., 9, 1996, 45-49.
%F A245826 T(m,n) = mn(2m^2 n^2 - m^2 - n^2)/6. See the Klavzar et al. reference; p. 47, line 6; there is a typo: n^2 - m^2 should be n^2 + m^2.
%e A245826 T(2,2) = 16 because P_2 X P_2 is the square C_4 and each of its 4 edges contributes 2*2=4 to its Szeged index.
%e A245826 Triangle starts:
%e A245826 0;
%e A245826 1,16;
%e A245826 4,59,216;
%e A245826 10,144,526,1280;
%e A245826 20,285,1040,2530,5000;
%p A245826 T:=proc(m,n) options operator, arrow: (1/6)*m*n*(2*m^2*n^2-m^2-n^2) end proc: for m to 12 do seq(T(m, n), n = 1 .. m) end do; # yields sequence in triangular form
%t A245826 T[m_, n_] := (1/6)*m*n*(2*m^2*n^2 - m^2 - n^2); Table[T[m, n], {m, 1, 12}, {n, 1, m}] // Flatten (* _Jean-François Alcover_, Feb 09 2018 *)
%o A245826 (Haskell)
%o A245826 a245826 n k = n * k * (2 * n^2 * k^2 - n^2 - k^2) `div` 6
%o A245826 a245826_row n = map (a245826 n) [1..n]
%o A245826 a245826_tabl = map a245826_row [1..]
%o A245826 -- _Reinhard Zumkeller_, Aug 07 2014
%Y A245826 Cf. A000292, A063521, A245827, A245828.
%Y A245826 Cf. A245940 (row sums), A245941 (central terms).
%K A245826 nonn,tabl
%O A245826 1,3
%A A245826 _Emeric Deutsch_, Aug 06 2014

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE