A309676 Number of compositions (ordered partitions) of n into odd primes (including 1).

1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 86, 138, 222, 357, 573, 921, 1481, 2381, 3828, 6153, 9890, 15898, 25556, 41082, 66039, 106156, 170644, 274307, 440945, 708815, 1139412, 1831589, 2944253, 4732847, 7607989, 12229743, 19659153, 31601828, 50799517, 81659549

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - x - Sum_{k>=2} x^prime(k)).

Maple

a:= proc(n) option remember; `if`(n=0, 1, a(n-1)+
      add(`if`(isprime(j), a(n-j), 0), j=3..n))
    end:
seq(a(n), n=0..42);  # Alois P. Heinz, Aug 12 2019

Mathematica

nmax = 42; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 2, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[Boole[PrimeOmega[k] < 2 && OddQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]

Crossrefs

Cf. A002124, A006005, A008578, A023360, A080545, A280917, A298603, A298604.

Sequence in context: A117760 A181600 A111917 * A280198 A175712 A013986

Adjacent sequences: A309673 A309674 A309675 * A309677 A309678 A309679

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 12 2019

Status

approved