|
%I #8 Jun 02 2017 00:29:27
%S 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,
%T 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,
%U 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
%N Number of partitions of n into primes which are the difference of two consecutive cubes (A002407).
%H G. C. Greubel, <a href="/A286935/b286935.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubanPrime.html">Cuban Prime</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexNumber.html">Hex 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^A002407(k)).
%e a(56) = 2 because we have [37, 19] and [7, 7, 7, 7, 7, 7, 7, 7].
%t nmax = 100; CoefficientList[Series[Product[1/(1 - x^k), {k, Select[(Range[nmax] + 1)^3 - Range[nmax]^3, PrimeQ]}], {x, 0, nmax}], x]
%Y Cf. A000607, A002407, A003215, A280953, A286934.
%K nonn
%O 0,57
%A _Ilya Gutkovskiy_, May 16 2017
|
