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A061197
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Table by antidiagonals T(n,k) of number of partitions of k where the largest part is less than or equal to n and where there are no more than two of any particular sized part.
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1
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1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 1, 3, 4, 2, 2, 1, 1, 0, 0, 0, 3, 4, 4, 2, 2, 1, 1, 0, 0, 0, 3, 5, 5, 4, 2, 2, 1, 1, 0, 0, 0, 3, 5, 6, 5, 4, 2, 2, 1, 1, 0, 0, 0, 2, 7, 7, 7, 5, 4, 2, 2, 1, 1, 0, 0, 0, 2, 6, 9, 8, 7, 5, 4, 2, 2, 1, 1
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OFFSET
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0,13
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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T(n, k)=T(n-1, k)+T(n-1, n-k)+T(n-1, n-2k) [with T(0, 0)=1 and T(n, k)=0 if n or k are negative].
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EXAMPLE
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Rows start (1,0,0,0,0,0,...), (1,1,1,0,0,0,...), (1,1,2,1,2,1,...), (1,1,2,2,3,3,...) etc. T(3,5)=3 since 5 can be written as 3+2 or 3+1+1 or 2+2+1.
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CROSSREFS
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Main diagonal is A000726.
Sequence in context: A025908 A134404 A107110 * A196346 A035178 A093829
Adjacent sequences: A061194 A061195 A061196 * A061198 A061199 A061200
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley, Apr 20 2001
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STATUS
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approved
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