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A261854
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Number of compositions of n into distinct parts where each part i is marked with a word of length i over a ternary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
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2
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7, 21, 96, 832, 1539, 4281, 10902, 76020, 117585, 306639, 634686, 1537206, 9013319, 13793487, 32005392, 64458596, 138068775, 278292429, 1622912266, 2321086080, 5318890971, 10014128239, 20784037248, 38209197732, 80154402633, 415073903937, 593664848658
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OFFSET
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3,1
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COMMENTS
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Also number of matrices with three rows of nonnegative integer entries and without zero rows or columns such that the sum of all entries is equal to n and the column sums are distinct.
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
`if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(3):
seq(a(n), n=3..40);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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