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A340964
Number of ways to write n as an ordered sum of 8 primes.
11
1, 8, 28, 64, 126, 232, 392, 624, 925, 1296, 1800, 2416, 3158, 4088, 5152, 6504, 8142, 9976, 12216, 14784, 17738, 21296, 25272, 29736, 35023, 40768, 47328, 54832, 62728, 71744, 81796, 92736, 105078, 118664, 132924, 149424, 167002, 186144, 206852, 229272, 253023
OFFSET
16,2
LINKS
FORMULA
G.f.: (Sum_{k>=1} x^prime(k))^8.
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, 8):
seq(a(n), n=16..56); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 56; CoefficientList[Series[Sum[x^Prime[k], {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 16] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved