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A320279 Number of partitions of 2*n into parts that are the average of twin prime pairs (A014574). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)