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A309676 Number of compositions (ordered partitions) of n into odd primes (including 1). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)