cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A301503 Number of compositions (ordered partitions) of n into square parts (A000290) such that no two adjacent parts are equal (Carlitz compositions).

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%I A301503 #4 Mar 22 2018 17:57:16
%S A301503 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 A301503 74,87,83,84,120,178,209,205,219,305,434,515,523,572,785,1080,1255,
%U A301503 1303,1488,2002,2644,3058,3284,3849,5077,6518,7525,8319,9927,12803,16051,18623,21081
%N A301503 Number of compositions (ordered partitions) of n into square parts (A000290) such that no two adjacent parts are equal (Carlitz compositions).
%H A301503 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H A301503 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A301503 G.f.: 1/(1 - Sum_{k>=1} x^(k^2)/(1 + x^(k^2))).
%e A301503 a(10) = 4 because we have [9, 1], [4, 1, 4, 1], [1, 9] and [1, 4, 1, 4].
%t A301503 nmax = 61; CoefficientList[Series[1/(1 - Sum[x^k^2/(1 + x^k^2), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y A301503 Cf. A000290, A003242, A006456, A301502.
%K A301503 nonn
%O A301503 0,6
%A A301503 _Ilya Gutkovskiy_, Mar 22 2018