A286934 Number of partitions of n into centered square primes (A027862).

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 1, 3, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 4, 4, 3, 3, 4, 4, 4, 3, 3, 5

Offset

0,42

Links

Table of n, a(n) for n=0..100.

Eric Weisstein's World of Mathematics, Centered Square 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^A027862(k)).

Example

a(41) = 2 because we have [41] and [13, 13, 5, 5, 5].

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^k), {k, Select[Range[nmax]^2 + (Range[nmax] + 1)^2, PrimeQ]}], {x, 0, nmax}], x]

Crossrefs

Cf. A000607, A001844, A027862, A280951, A282970.

Sequence in context: A226194 A053692 A341024 * A282714 A280634 A281491

Adjacent sequences: A286931 A286932 A286933 * A286935 A286936 A286937

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2017

Status

approved