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Number of partitions of n into distinct fourth powers.
4

%I #5 Jan 28 2018 11:02:25

%S 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1

%N Number of partitions of n into distinct fourth powers.

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

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} (1 + x^(k^4)).

%t nmax = 98; CoefficientList[Series[Product[1 + x^k^4, {k, 1, Floor[nmax^(1/4) + 1]}], {x, 0, nmax}], x]

%Y Cf. A000009, A000583, A002377, A003999, A033461, A046039 (positions of zeros), A046042, A259793, A279329, A279485.

%K nonn

%O 0

%A _Ilya Gutkovskiy_, Jan 27 2018