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%I #7 Jan 19 2017 06:03:23
%S 0,1,2,1,0,2,2,0,0,1,0,0,0,0,2,2,0,0,2,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,2,2,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Expansion of (Sum_{k>=0} x^(3^k))^2 [even terms only].
%C Number of ways to write 2n as an ordered sum of two powers of 3.
%C First bisection of self-convolution of characteristic function of powers of 3.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: (Sum_{k>=0} x^(3^k))^2 [even terms only].
%e G.f. = x^2 + 2*x^4 + x^6 + 2*x^10 + 2*x^12 + x^18 + 2*x^28 + 2*x^30 + 2*x^36 + ...
%e a(2) = 2 because we have [3, 1] and [1, 3].
%t Take[CoefficientList[Series[Sum[x^3^k, {k, 0, 15}]^2, {x, 0, 260}], x], {1, -1, 2}]
%Y Cf. A000244, A055235, A073267, A078932.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jan 18 2017
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