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A374728
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Number of n-color gap-free compositions of n.
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3
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1, 1, 1, 3, 7, 19, 45, 105, 239, 507, 1079, 2303, 4829, 10425, 23263, 53363, 127995, 318983, 816057, 2133241, 5640135, 14975051, 39772751, 105322879, 277547989, 727276225, 1894282195, 4903985955, 12621154315, 32302574959, 82248961437, 208426306113, 525884062427
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OFFSET
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1,4
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COMMENTS
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These are integer compositions whose set of parts covers some interval and contains k colors of each part k.
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LINKS
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EXAMPLE
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a(5) = 7 counts: (1,1,1,1,1), (1,2_a,2_b), (1,2_b,2_a), (2_a,1,2_b), (2_a,2_b,1), (2_b,1,2_a), (2_b,2_a,1).
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PROG
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(PARI)
colr(x, y)={my(r=y-x+1, v=[x..y], z = vector(r*(r+(1+(x-1)*2))/2), k=1); for(i=1, #v, for(j=1, v[i], z[k]=v[i]; k++)); return(z)}
C_x(s, N)={my(x='x+O('x^N), g=if(#s <1, 1, sum(i=1, #s, C_x(s[^i], N+1) * x^(s[i]) )/(1-sum(i=1, #s, x^(s[i]))))); return(g)}
B_x(N)={my(x='x+O('x^N), h=0); for(u=1, N, my(j=0); while(vecsum(colr(u, u+j)) <= N, h += C_x(colr(u, u+j), N+1); j++)); my(a = Vec(h)); vector(N, i, a[i])}
B_x(20)
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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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