A339165 Number of compositions (ordered partitions) of n into distinct parts, the least being 4.

0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 50, 56, 80, 110, 134, 164, 212, 242, 410, 464, 632, 806, 1118, 1292, 1724, 2042, 2594, 3752, 4448, 5726, 7382, 9524, 12020, 15122, 18602, 23264, 28424, 39830, 46670, 60476, 74780

Offset

0,10

Links

Table of n, a(n) for n=0..52.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=1} k! * x^(k*(k + 7)/2) / Product_{j=1..k-1} (1 - x^j).

Example

a(15) = 8 because we have [11, 4], [6, 5, 4], [6, 4, 5], [5, 6, 4], [5, 4, 6], [4, 11], [4, 6, 5] and [4, 5, 6].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-4)*(i+5)/2<n, 0,
       add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
    end:
a:= n-> `if`(n<4, 0, b(n-4$2, 1)):
seq(a(n), n=0..55);  # Alois P. Heinz, Nov 25 2020

Mathematica

nmax = 52; CoefficientList[Series[Sum[k! x^(k (k + 7)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026797, A026825, A339102, A339162, A339163, A339164, A339166.

Sequence in context: A172009 A299150 A202448 * A129381 A319991 A323275

Adjacent sequences: A339162 A339163 A339164 * A339166 A339167 A339168

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 25 2020

Status

approved