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A305556
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Irregular triangle read by rows: T(n,k) is the number of superdiagonal bargraphs with area n and with k columns.
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2
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1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 5, 3, 1, 6, 6, 1, 7, 10, 1, 8, 15, 1, 1, 9, 21, 4, 1, 10, 28, 10, 1, 11, 36, 20, 1, 12, 45, 35, 1, 13, 55, 56, 1, 1, 14, 66, 84, 5, 1, 15, 78, 120, 15, 1, 16, 91, 165, 35, 1, 17, 105, 220, 70, 1, 18, 120, 286, 126, 1, 19, 136, 364, 210, 1, 1, 20, 153, 455
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OFFSET
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1,6
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LINKS
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Emeric Deutsch, Emanuele Munarini, Simone Rinaldi, Skew Dyck paths, area, and superdiagonal bargraphs, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562.
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FORMULA
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T(n,k) = binomial(n-1-k*(k-1)/2,k-1), 1<=k <= (sqrt(1+8*n)-1)/2.
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EXAMPLE
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1,
1,
1, 1,
1, 2,
1, 3,
1, 4, 1,
1, 5, 3,
1, 6, 6,
1, 7, 10,
1, 8, 15, 1,
1, 9, 21, 4,
1, 10, 28, 10,
1, 11, 36, 20,
1, 12, 45, 35,
1, 13, 55, 56, 1,
1, 14, 66, 84, 5,
1, 15, 78, 120, 15,
1, 16, 91, 165, 35,
1, 17, 105, 220, 70,
1, 18, 120, 286, 126,
1, 19, 136, 364, 210, 1,
1, 20, 153, 455, 330, 6,
1, 21, 171, 560, 495, 21,
1, 22, 190, 680, 715, 56,
1, 23, 210, 816,1001, 126,
1, 24, 231, 969,1365, 252,
1, 25, 253,1140,1820, 462,
1, 26, 276,1330,2380, 792, 1,
1, 27, 300,1540,3060,1287, 7,
1, 28, 325,1771,3876,2002, 28,
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MAPLE
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binomial(n-binomial(k, 2)-1, k-1) ;
end proc:
for n from 0 to 30 do
for k from 1 to floor((sqrt(1+8*n)-1)/2) do
end do:
end do:
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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