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Search: id:A059623
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| A059623 |
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As upper right triangle, number of weakly unimodal partitions of n (weakly unimodal means non-decreasing then non-increasing) where initial part is k (n >= k >= 1). |
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3
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| 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 3, 2, 1, 1, 15, 5, 3, 2, 1, 1, 27, 8, 5, 3, 2, 1, 1, 47, 13, 7, 5, 3, 2, 1, 1, 79, 21, 11, 7, 5, 3, 2, 1, 1, 130, 33, 16, 11, 7, 5, 3, 2, 1, 1, 209, 52, 24, 15, 11, 7, 5, 3, 2, 1, 1, 330, 80, 35, 22, 15, 11, 7, 5, 3, 2, 1, 1, 512, 122, 52, 31, 22, 15, 11, 7, 5, 3
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OFFSET
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1,4
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FORMULA
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T(n, k)=S(n, k)-S(n-k, k)+sum_j[T(n-k, j)] for j >= k, where S(n, k)=A008284(n, k)=sum_j[S(n-k, j)] for n>k >= j [note reversal] with S[n, n]=1.
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EXAMPLE
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Rows are: {1,1,2,4,8,15,...}, {1,1,2,3,5,8,...}, {1,1,2,3,5,7,...} etc. T(9,3)=11 since 9 can be written as 3+6, 3+5+1, 3+4+2, 3+4+1+1, 3+3+3, 3+3+2+1, 3+3+1+1+1, 3+2+2+2, 3+2+2+1+1, 3+2+1+1+1+1 or 3+1+1+1+1+1.
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CROSSREFS
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Column sums give A001523. Cf. A008284, A026836, A008284, A059607, A059619.
Sequence in context: A140998 A048004 A114394 this_sequence A140997 A140996 A141020
Adjacent sequences: A059620 A059621 A059622 this_sequence A059624 A059625 A059626
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 01 2001
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