A299197 Number of partitions of n into distinct parts that are greater of twin primes (A006512).

1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 1, 3, 1, 1, 0, 0, 2, 3, 2, 0, 0, 1, 2, 3, 2, 1, 0, 0, 2, 3, 3, 0, 0, 0, 1, 4, 3, 1, 0, 0, 2, 3, 3, 2, 0, 0, 1, 4, 4

Offset: 0

Author

Ilya Gutkovskiy, Feb 04 2018

Keywords

• nonn

Examples

			a(31) = 2 because we have [31] and [19, 7, 5].
		

Links

• Eric Weisstein's World of Mathematics, Twin Primes
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000586, A000607, A001097, A006512, A077608, A129363, A283875, A283876, A299196.

Programs

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + Boole[PrimeQ[k] && PrimeQ[k - 2]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + x^A006512(k)).