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A083504 Triangle read by rows: for 1 <= k <= n, T(n, k) is the total perimeter of all squares contained in a square grid with n rows and k columns.

%I A083504 #4 Mar 31 2012 13:20:47
%S A083504 4,8,24,12,40,80,16,56,120,200,20,72,160,280,420,24,88,200,360,560,
%T A083504 784,28,104,240,440,700,1008,1344,32,120,280,520,840,1232,1680,2160,
%U A083504 36,136,320,600,980,1456,2016,2640,3300,40,152,360,680,1120,1680,2352,3120
%N A083504 Triangle read by rows: for 1 <= k <= n, T(n, k) is the total perimeter of all squares contained in a square grid with n rows and k columns.
%C A083504 T(n, n) = 4*A002415(n+1). Row sums are 4*A051836.
%F A083504 T(n, k) = (2k^3*n+6k^2*n+k^2+4k*n+2k-k^4-2k^3)/3.
%e A083504 T(3, 2) = 40 because the six 1 X 1 squares each have perimeter 4 and the two 2 X 2 squares each have perimeter 8.
%Y A083504 Cf. A082652, A083003.
%K A083504 nonn,tabl,easy
%O A083504 1,1
%A A083504 Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Jun 09 2003
%E A083504 Edited by _David Wasserman_, Nov 18 2004