A340966 Number of ways to write n as an ordered sum of 10 primes.

1, 10, 45, 130, 300, 622, 1185, 2100, 3495, 5480, 8266, 12100, 17140, 23730, 32155, 42802, 56400, 73180, 93820, 119250, 149872, 187090, 231765, 284490, 347335, 421332, 507580, 608840, 725500, 859450, 1014473, 1190700, 1392100, 1621710, 1879950, 2172610, 2503580

Offset

20,2

Links

Seiichi Manyama, Table of n, a(n) for n = 20..10000

Formula

G.f.: (Sum_{k>=1} x^prime(k))^10.

Maple

b:= proc(n, k) option remember; local r, p; r, p:= 0, 2;
      if n=0 then `if`(k=0, 1, 0) elif k<1 then 0 else
      while p<=n do r:= r+b(n-p, k-1); p:= nextprime(p) od; r fi
    end:
a:= n-> b(n, 10):
seq(a(n), n=20..56);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 20] &

Crossrefs

Column k=10 of A121303.

Cf. A000040, A010051, A073610, A098238, A259201, A340960, A340961, A340962, A340963, A340964, A340965.

Sequence in context: A105938 A342254 A226254 * A022605 A211032 A179095

Adjacent sequences: A340963 A340964 A340965 * A340967 A340968 A340969

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved