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A082652
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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.
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5
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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, 112, 140, 8, 23, 44, 70, 100, 133, 168, 204, 9, 26, 50, 80, 115, 154, 196, 240, 285, 10, 29, 56, 90, 130, 175, 224, 276, 330, 385, 11, 32, 62, 100, 145, 196, 252, 312, 375, 440
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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).
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 85 112 140
Here the squares being counted have sides parallel to the gridlines; for all squares, see A130684.
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FORMULA
| T(l, c) = ( c + 3*c*l + 3*c^2*l - c^3 ) / 6
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
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EXAMPLE
| Let X represent a small square. Then T(3,2) = 8 because here
XXX
XXX
we can see 8 squares, 6 of side 1, 2 of side 2.
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MAPLE
| f:=proc(m, n) add((m-i)*(n-i), i=0..min(m, n)); end;
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CROSSREFS
| Cf. A083003, A083487. Right side of triangle gives A000330.
Main diagonal is A000330, row sums are A001296. - Paul D. Hanna (pauldhanna(AT)juno.com) and other correspondents, May 28, 2003
Cf. A130684. - Joel B. Lewis (jblewis(AT)post.harvard.edu)
Sequence in context: A050171 A136189 A081146 * A194007 A065222 A159988
Adjacent sequences: A082649 A082650 A082651 * A082653 A082654 A082655
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KEYWORD
| nonn,tabl
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AUTHOR
| Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), May 16 2003
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