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A376348
a(n) is the number of multisets with n primes with which an n-gon with perimeter prime(n) can be formed.
1
0, 0, 1, 1, 2, 2, 3, 7, 7, 12, 19, 19, 25, 44, 72, 72, 119, 147, 152, 234, 292, 435, 777, 920, 946, 1135, 1161, 1377, 3702, 4293, 5942, 5942, 10741, 10741, 14483, 18953, 22091, 28658, 37686, 37686, 63053, 63053, 72389, 72389, 132732, 233773, 265312, 265312, 300443, 373266
OFFSET
3,5
COMMENTS
a(n) is the number of partitions of prime(n) into n prime parts < prime(n)/2.
First differs from A259254 at n=31: a(31) = 3702 but A259254(31) = 3703.
LINKS
Eric Weisstein's World of Mathematics, Polygon
EXAMPLE
a(7) = 2 because exactly the 2 partitions (2, 2, 2, 2, 3, 3, 3) and (2, 2, 2, 2, 2, 2, 5) have 7 prime parts and their sum is p(7) = 17.
MAPLE
A376348:=proc(n)
local a, p, x, i;
a:=0;
p:=ithprime(n);
for x from NumberTheory:-pi(p/n)+1 to NumberTheory:-pi(p/2) do
a:=a+numelems(select(i->nops(i)=n-1 and andmap(isprime, i), combinat:-partition(ithprime(n)-ithprime(x), ithprime(x))))
od;
return a
end proc;
seq(A376348(n), n=3..42);
PROG
(PARI) a(n)={my(m=prime(n), p=primes(primepi((m-1)\2))); polcoef(polcoef(1/prod(i=1, #p, 1 - y*x^p[i], 1 + O(x*x^m)), m), n)} \\ Andrew Howroyd, Oct 13 2024
KEYWORD
nonn
AUTHOR
Felix Huber, Oct 13 2024
EXTENSIONS
a(43) onwards from Andrew Howroyd, Oct 13 2024
STATUS
approved