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A261855
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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 quaternary 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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9, 92, 1562, 3908, 14791, 50208, 540552, 987120, 3138143, 7862580, 23436690, 204455140, 349297653, 956040232, 2228084512, 5599922904, 13449425997, 116772809532, 182990434794, 483410072060, 1033025269277, 2455590595520, 5184309618676, 12755194552152
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OFFSET
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4,1
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COMMENTS
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Also number of matrices with four 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))(4):
seq(a(n), n=4..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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