A374727 Number of n-color complete compositions of n.

1, 1, 1, 1, 7, 13, 45, 91, 233, 477, 1079, 2205, 4709, 10299, 22393, 52005, 125055, 310373, 799677, 2096699, 5556681, 14806685, 39417431, 104570549, 276027337, 724183555, 1887993925, 4891368373, 12595644523, 32252683453, 82146468813, 208225916203, 525472131209

Offset

1,5

Comments

These are integer compositions whose set of parts covers an initial interval and contains k colors of each part k.

Links

Table of n, a(n) for n=1..33.

Example

a(6) = 13 counts: (1,1,1,1,1,1) and the 12 permutations of parts 1, 1, 2_a, and 2_b.

Prog

(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) * x^(s[i]) )/(1-sum(i=1, #s, x^(s[i]))))); return(g)}
B_x(N)={my(x='x+O('x^N), j=1, h=0, s=colr(1, j)); while(vecsum(s) <= N, h += C_x(s, N+1); j++; s=colr(1, j)); my(a = Vec(h)); vector(N, i, a[i])}
B_x(25)

Crossrefs

Cf. A003242, A011782, A107428, A107429, A374147, A374726, A374728.

Sequence in context: A287685 A159305 A146648 * A219501 A267310 A153119

Adjacent sequences: A374716 A374718 A374726 * A374728 A374729 A374735

Keyword

nonn,new

Author

John Tyler Rascoe, Jul 17 2024

Status

approved