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A140765
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Array T(n,k) = binomial(k+2,k-1)+n*binomial(k+2,k) read by antidiagonals.
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1
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0, 1, 1, 2, 4, 4, 3, 7, 10, 10, 4, 10, 16, 20, 20, 5, 13, 22, 30, 35, 35, 6, 16, 28, 40, 50, 56, 56, 7, 19, 34, 50, 65, 77, 84, 84, 8, 22, 40, 60, 80, 98, 112, 120, 120, 9, 25, 46, 70, 95, 119, 140, 156, 165, 165, 10, 28, 52, 80, 110, 140, 168, 192, 210, 220, 220, 11, 31, 58
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| D. A. Sardelis, T. M. Valahas, On Multidimensional Pythagorean Numbers, arxiv:0805.4070, Table 6, eq 12.
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FORMULA
| T(n,k) = binomial(k+2,3)+n*binomial(k+2,2).
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EXAMPLE
| The array starts in row n=0 with columns k>=0 as
0,1,4,10,20,35,56,84,120,165,220,
1,4,10,20,35,56,84,120,165,220,286,
2,7,16,30,50,77,112,156,210,275,352,
3,10,22,40,65,98,140,192,255,330,418,
4,13,28,50,80,119,168,228,300,385,484,
5,16,34,60,95,140,196,264,345,440,550,
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MAPLE
| A140765 := proc(n, k) binomial(k+2, k-1)+n*binomial(k+2, k) ; end proc:
# R. J. Mathar, Aug 31 2011
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CROSSREFS
| Sequence in context: A098217 A151846 A131118 * A097541 A151819 A079560
Adjacent sequences: A140762 A140763 A140764 * A140766 A140767 A140768
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 28 2008
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EXTENSIONS
| Definition substantiated by R. J. Mathar, Aug 31 2011
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