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A286934 Number of partitions of n into centered square primes (A027862). 1

%I #4 May 17 2017 11:36:52

%S 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,

%T 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,

%U 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

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredSquareNumber.html">Centered Square Number</a>

%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: Product_{k>=1} 1/(1 - x^A027862(k)).

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

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

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

%K nonn

%O 0,42

%A _Ilya Gutkovskiy_, May 16 2017

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)