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A343756 Number of nondecreasing sequences s1, s2, ..., s_n of powers of 2 such that s_i <= 1 + Sum_{j=1..i-1} s_j.

%I A343756 #16 Apr 30 2021 20:14:56
%S A343756 1,1,2,4,9,20,45,102,232,528,1203,2742,6252,14258,32519,74173,169189,
%T A343756 385929,880337,2008141,4580803,10449377,23836364,54373853,124033933,
%U A343756 282937887,645419092,1472287344,3358484832,7661154644,17476122569,39865383333,90938296121
%N A343756 Number of nondecreasing sequences s1, s2, ..., s_n of powers of 2 such that s_i <= 1 + Sum_{j=1..i-1} s_j.
%H A343756 Alois P. Heinz, <a href="/A343756/b343756.txt">Table of n, a(n) for n = 0..2793</a>
%e A343756 a(0) = 1: [].
%e A343756 a(1) = 1: [1].
%e A343756 a(2) = 2: [1,1], [1,2].
%e A343756 a(3) = 4: [1,1,1], [1,1,2], [1,2,2], [1,2,4].
%e A343756 a(4) = 9 : [1,1,1,1], [1,1,1,2], [1,1,1,4], [1,1,2,2], [1,1,2,4], [1,2,2,2], [1,2,2,4], [1,2,4,4], [1,2,4,8].
%e A343756 a(5) = 20: [1,1,1,1,1], [1,1,1,1,2], [1,1,1,1,4], [1,1,1,2,2], [1,1,1,2,4], [1,1,1,4,4], [1,1,1,4,8], [1,1,2,2,2], [1,1,2,2,4], [1,1,2,4,4], [1,1,2,4,8], [1,2,2,2,2], [1,2,2,2,4], [1,2,2,2,8], [1,2,2,4,4], [1,2,2,4,8], [1,2,4,4,4], [1,2,4,4,8], [1,2,4,8,8], [1,2,4,8,16].
%p A343756 b:= proc(n, t) option remember; `if`(n=0, 1,
%p A343756      `if`(t=0, 0, b(n, iquo(t, 2))+b(n-1, t+1)))
%p A343756     end:
%p A343756 a:= n-> b(n, 1):
%p A343756 seq(a(n), n=0..38);
%Y A343756 Cf. A000079, A339479, A343799, A343820.
%K A343756 nonn
%O A343756 0,3
%A A343756 _Alois P. Heinz_, Apr 27 2021