|
%I #4 Mar 22 2018 17:57:16
%S 1,1,0,0,1,2,1,0,0,2,4,2,0,2,7,8,4,3,7,14,16,11,9,18,32,35,30,32,49,
%T 74,87,83,84,120,178,209,205,219,305,434,515,523,572,785,1080,1255,
%U 1303,1488,2002,2644,3058,3284,3849,5077,6518,7525,8319,9927,12803,16051,18623,21081
%N Number of compositions (ordered partitions) of n into square parts (A000290) such that no two adjacent parts are equal (Carlitz compositions).
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F G.f.: 1/(1 - Sum_{k>=1} x^(k^2)/(1 + x^(k^2))).
%e a(10) = 4 because we have [9, 1], [4, 1, 4, 1], [1, 9] and [1, 4, 1, 4].
%t nmax = 61; CoefficientList[Series[1/(1 - Sum[x^k^2/(1 + x^k^2), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A000290, A003242, A006456, A301502.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Mar 22 2018
|
