A318604 -id:A318604 - cp's OEIS frontend

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

Felix Huber, Oct 13 2024

nonn

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.

			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.

Eric Weisstein's World of Mathematics, Polygon

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

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);

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

Extensions