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

0,7

Links

Table of n, a(n) for n=0..65.

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for sequences related to partitions

Formula

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

Example

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

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}]

Crossrefs

Cf. A001097, A014574, A283875.

Sequence in context: A219525 A050121 A029152 * A175290 A089958 A162932

Adjacent sequences: A320276 A320277 A320278 * A320280 A320281 A320282

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 25 2018

Status

approved