A282583 - OEIS

%I #7 Mar 15 2017 20:26:41

%S 1,1,2,3,6,10,19,33,60,107,193,345,621,1113,1999,3586,6439,11554,

%T 20741,37223,66814,119916,215237,386310,693375,1244494,2233686,

%U 4009113,7195757,12915268,23180946,41606232,74676840,134033474,240569601,431785583,774989076,1390986741,2496608365,4481029864,8042762869

%N Number of compositions (ordered partitions) of n into quarter-squares (A002620).

%H Indranil Ghosh, <a href="/A282583/b282583.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: 1/(1 - Sum_{k>=2} x^(floor(k^2/4))).

%e a(4) = 6 because we have [4], [2, 2], [2, 1, 1], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].

%t nmax = 40; CoefficientList[Series[1/(1 - Sum[x^Floor[k^2/4], {k, 2, nmax}]), {x, 0, nmax}], x]

%o (PARI) Vec(1/(1 - sum(k=2, 40, x^floor(k^2/4)) + O(x^41))) \\ _Indranil Ghosh_, Mar 15 2017

%Y Cf. A002620, A006456, A197081, A197122.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 19 2017