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.
%I A385604 #9 Aug 05 2025 10:02:17
%S A385604 1,1,2,4,7,14,25,48,86,162,292,541,978,1794,3247,5919,10712,19451,
%T A385604 35184,63729,115199,208327,376333,679842,1227403,2215695,3998408,
%U A385604 7214274,13014001,23472678,42331028,76330880,137627168,248122171,447301570,806312371,1453405651
%N A385604 Number of compositions of n such that the odd parts are weakly increasing.
%F A385604 G.f.: (1 - x^2)/( (1 - 2*x^2) * Product_{i>=0} (1 - x^(2*i + 1) * (1 - x^2)/(1 - 2*x^2)) ).
%e A385604 a(5) = 14 counts all compositions of n = 5 except (1,3,1) and (3,1,1) since the odd parts are not weakly increasing.
%e A385604 The composition of n = 13 (2,1,1,4,2,3) has odd parts (1,1,3), so it is counted under a(13) = 1794.
%o A385604 (PARI) A_x(N) = {my(x='x+O('x^(N+1))); Vec((1-x^2)/(1-2*x^2)/prod(i=0,N, 1-x^(2*i+1)*(1-x^2)/(1-2*x^2)))}
%Y A385604 Cf. A000009, A011782, A032021, A098123, A289249.
%K A385604 nonn,easy
%O A385604 0,3
%A A385604 _John Tyler Rascoe_, Aug 02 2025