%I A082652
%S A082652 1,2,5,3,8,14,4,11,20,30,5,14,26,40,55,6,17,32,50,70,91,7,20,38,60,85,
%T A082652 112,140,8,23,44,70,100,133,168,204,9,26,50,80,115,154,196,240,285,10,
%U A082652 29,56,90,130,175,224,276,330,385,11,32,62,100,145,196,252,312,375,440
%N A082652 Triangle read by rows: T(l,c) = number of squares that can be found in 
               a c X l rectangular grid of little squares, for 1 <= c <= l.
%C A082652 T(l,c) also is the total number of balls in a pyramid of balls on an 
               l X c rectangular base. - N. J. A. Sloane (njas(AT)research.att.com), 
               Nov 17 2007. For example, if the base is 4 X 2, the total number 
               of balls is 4*2 + 3*1 = 11 = T(4,2).
%C A082652 1
%C A082652 2 5
%C A082652 3 8 14
%C A082652 4 11 20 30
%C A082652 5 14 26 40 55
%C A082652 6 17 32 50 70 91
%C A082652 7 20 38 60 85 112 140
%F A082652 T(l, c) = ( c + 3*c*l + 3*c^2*l - c^3 ) / 6
%F A082652 T(l, c) = Sum{ i = 0..min(l,c)} (l-i)*(c-i). - N. J. A. Sloane (njas(AT)research.att.com), 
               Nov 17, 2007
%e A082652 Let X represent a small square. Then T(3,2) = 8 because here
%e A082652 XXX
%e A082652 XXX
%e A082652 we can see 8 squares, 6 of side 1, 2 of side 2.
%p A082652 f:=proc(m,n) add((m-i)*(n-i),i=0..min(m,n)); end;
%Y A082652 Cf. A083003, A083487. Right side of triangle gives A000330.
%Y A082652 Main diagonal is A000330, row sums are A001296. - Paul D. Hanna (pauldhanna(AT)juno.com) 
               and other correspondents, May 28, 2003
%Y A082652 Sequence in context: A050171 A136189 A081146 this_sequence A065222 A159988 
               A134880
%Y A082652 Adjacent sequences: A082649 A082650 A082651 this_sequence A082653 A082654 
               A082655
%K A082652 nonn,tabl
%O A082652 1,2
%A A082652 Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), May 16 2003