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A104633
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Triangle T(n,k) = k*(k-n-1)*(k-n-2)/2 read by rows, 1<=k<=n.
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3
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1, 3, 2, 6, 6, 3, 10, 12, 9, 4, 15, 20, 18, 12, 5, 21, 30, 30, 24, 15, 6, 28, 42, 45, 40, 30, 18, 7, 36, 56, 63, 60, 50, 36, 21, 8, 45, 72, 84, 84, 75, 60, 42, 24, 9, 55, 90, 108, 112, 105, 90, 70, 48, 27, 10, 66, 110, 135
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The triangle can be constructed multiplying the triangle A(n,k)=n-k+1 (if 1<=k<=n, else 0) by the triangle B(n,k) =k (if 1<=k<=n, else 0).
Swapping the two triangles of this matrix product would generate A104634.
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EXAMPLE
| First few rows of the triangle:
1;
3, 2;
6, 6, 3;
10, 12, 9, 4;
15, 20, 18, 12, 5;
21, 30, 30, 24, 15, 6;
28, 42, 45, 40, 30, 18, 7;
36, 56, 63, 60, 50, 36, 21, 8;
...
e.g. Col. 3 = 3 * (1, 3, 6, 10, 15...) = 3, 9, 18, 30, 45...
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MAPLE
| A104633 := proc(n, k) k*(k-n-1)*(k-n-2)/2 ; end proc:
seq(seq(A104633(n, k), k=1..n), n=1..16) ; # R. J. Mathar, Mar 03 2011
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CROSSREFS
| Cf. A062707, A158824, A104634, A001296, A000332 (row sums)
Sequence in context: A189073 A107271 A196565 * A102022 A064684 A098071
Adjacent sequences: A104630 A104631 A104632 * A104634 A104635 A104636
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 18 2005
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