A341986 Number of ways to write n as an ordered sum of 7 primes (counting 1 as a prime).

1, 7, 28, 77, 168, 308, 511, 785, 1155, 1603, 2142, 2723, 3430, 4207, 5202, 6216, 7497, 8729, 10451, 12061, 14350, 16205, 19033, 21182, 24934, 27482, 32109, 34587, 40139, 42714, 49791, 52290, 60718, 62699, 73297, 75278, 88571, 89488, 104993, 104482, 123760, 122066

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..10000

Formula

G.f.: ( x + Sum_{k>=1} x^prime(k) )^7.

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
      `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 8)
    end:
a:= n-> coeff(b(n), x, 7):
seq(a(n), n=7..48);  # Alois P. Heinz, Feb 25 2021

Mathematica

nmax = 48; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

Crossrefs

Cf. A008578, A280917, A283762, A340963, A341950, A341978, A341982, A341983, A341984, A341985, A341987, A341988, A341989.

Sequence in context: A211899 A073995 A357694 * A341067 A061968 A223772

Adjacent sequences: A341983 A341984 A341985 * A341987 A341988 A341989

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved