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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
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
Sequence in context: A117760 A181600 A111917 * A280198 A175712 A013986
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 12 2019
STATUS
approved

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Last modified April 23 22:36 EDT 2024. Contains 371917 sequences. (Running on oeis4.)