A385604 Number of compositions of n such that the odd parts are weakly increasing.
1, 1, 2, 4, 7, 14, 25, 48, 86, 162, 292, 541, 978, 1794, 3247, 5919, 10712, 19451, 35184, 63729, 115199, 208327, 376333, 679842, 1227403, 2215695, 3998408, 7214274, 13014001, 23472678, 42331028, 76330880, 137627168, 248122171, 447301570, 806312371, 1453405651
Offset: 0
Examples
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. 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.
Programs
-
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)))}
Formula
G.f.: (1 - x^2)/( (1 - 2*x^2) * Product_{i>=0} (1 - x^(2*i + 1) * (1 - x^2)/(1 - 2*x^2)) ).