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%I #8 Mar 21 2018 20:31:19
%S 1,0,1,1,0,3,0,4,3,3,10,3,16,12,18,35,24,64,57,90,137,136,259,270,416,
%T 573,679,1088,1264,1869,2491,3199,4691,5834,8341,11053,14685,20595,
%U 26636,37199,49449,66572,91377,120733,166151,221912,300038,407775,544843,743318,996752
%N Number of compositions (ordered partitions) of n into prime parts such that no two adjacent parts are equal (Carlitz compositions).
%H Alois P. Heinz, <a href="/A301428/b301428.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=1} x^prime(k)/(1 + x^prime(k))).
%e a(7) = 4 because we have [7], [5, 2], [2, 5] and [2, 3, 2].
%t nmax = 50; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A003242, A023360, A218694, A219107.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Mar 21 2018
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