A339408 Number of compositions (ordered partitions) of n into an even number of primes.

1, 0, 0, 0, 1, 2, 1, 2, 3, 6, 9, 8, 16, 24, 40, 52, 72, 112, 172, 256, 364, 528, 804, 1188, 1757, 2548, 3782, 5614, 8308, 12214, 17979, 26586, 39352, 58044, 85608, 126248, 186630, 275556, 406737, 600066, 885952, 1308250, 1931473, 2850692, 4207952, 6212110, 9171800, 13538980

Offset

0,6

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to compositions

Formula

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

Example

a(8) = 3 because we have [5, 3], [3, 5] and [2, 2, 2, 2].

Maple

b:= proc(n, t) option remember; `if`(n=0, t, add(
      b(n-ithprime(j), 1-t), j=1..numtheory[pi](n)))
    end:
a:= n-> b(n, 1):
seq(a(n), n=0..55);  # Alois P. Heinz, Dec 03 2020

Mathematica

nmax = 47; CoefficientList[Series[(1/2) (1/(1 - Sum[x^Prime[k], {k, 1, nmax}]) + 1/(1 + Sum[x^Prime[k], {k, 1, nmax}])), {x, 0, nmax}], x]

Crossrefs

Cf. A000040, A023360, A034008, A184198, A339380, A339409.

Sequence in context: A289352 A277619 A001371 * A277629 A277631 A277633

Adjacent sequences: A339405 A339406 A339407 * A339409 A339410 A339411

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 03 2020

Status

approved