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.

1, 1, 2, 4, 9, 20, 45, 102, 232, 528, 1203, 2742, 6252, 14258, 32519, 74173, 169189, 385929, 880337, 2008141, 4580803, 10449377, 23836364, 54373853, 124033933, 282937887, 645419092, 1472287344, 3358484832, 7661154644, 17476122569, 39865383333, 90938296121

Offset: 0

Author

Alois P. Heinz, Apr 27 2021

Keywords

• nonn

Examples

			a(0) = 1: [].
a(1) = 1: [1].
a(2) = 2: [1,1], [1,2].
a(3) = 4: [1,1,1], [1,1,2], [1,2,2], [1,2,4].
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].
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].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2793

Crossrefs

Cf. A000079, A339479, A343799, A343820.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, 1,
     `if`(t=0, 0, b(n, iquo(t, 2))+b(n-1, t+1)))
    end:
a:= n-> b(n, 1):
seq(a(n), n=0..38);