A376348 a(n) is the number of multisets with n primes with which an n-gon with perimeter prime(n) can be formed.

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

Table of n, a(n) for n=3..52.

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

Crossrefs

Cf. A005044, A007042, A038499, A062890, A069906, A069907, A259254, A288253, A288254, A288255, A288256, A318604, A366398.

Sequence in context: A342848 A339826 A108041 * A259254 A095017 A141559

Adjacent sequences: A376345 A376346 A376347 * A376349 A376350 A376351

Keyword

nonn

Author

Felix Huber, Oct 13 2024

Extensions

a(43) onwards from Andrew Howroyd, Oct 13 2024

Status

approved