A320279 Number of partitions of 2*n into parts that are the average of twin prime pairs (A014574).

1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 3, 4, 7, 4, 7, 10, 7, 10, 15, 10, 15, 21, 15, 21, 29, 21, 29, 39, 29, 39, 53, 39, 53, 68, 53, 68, 91, 68, 91, 114, 91, 114, 148, 114, 148, 184, 148, 184, 232, 184, 232, 287, 232, 287, 355, 287, 355, 434, 355, 434, 531, 434, 531, 641, 531, 641

Offset: 0

Author

Ilya Gutkovskiy, Oct 25 2018

Keywords

• nonn

Examples

			a(10) = 3 because we have [12, 4, 4], [6, 6, 4, 4] and [4, 4, 4, 4, 4].
		

Links

• Eric Weisstein's World of Mathematics, Twin Primes
• Index entries for sequences related to partitions

Crossrefs

Cf. A001097, A014574, A283875.

Programs

Mathematica

nmax = 65; Table[CoefficientList[Series[Product[1/(1 - Boole[PrimeQ[k + 1] && PrimeQ[k - 1]] x^k), {k, 1, 2 nmax}], {x, 0, 2 nmax}], x][[n]], {n, 1, 2 nmax + 1, 2}]

Formula

a(n) = [x^(2*n)] Product_{k>=1} 1/(1 - x^A014574(k)).