A286935 Number of partitions of n into primes which are the difference of two consecutive cubes (A002407).

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

Offset

0,57

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Cuban Prime

Eric Weisstein's World of Mathematics, Hex Number

Index entries for sequences related to centered polygonal numbers

Index entries for sequences related to partitions

Formula

G.f.: Product_{k>=1} 1/(1 - x^A002407(k)).

Example

a(56) = 2 because we have [37, 19] and [7, 7, 7, 7, 7, 7, 7, 7].

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^k), {k, Select[(Range[nmax] + 1)^3 - Range[nmax]^3, PrimeQ]}], {x, 0, nmax}], x]

Crossrefs

Cf. A000607, A002407, A003215, A280953, A286934.

Sequence in context: A064744 A135997 A026609 * A090340 A287364 A340676

Adjacent sequences: A286932 A286933 A286934 * A286936 A286937 A286938

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2017

Status

approved