A173404 Number of partitions of 1 into up to n powers of 1/2.

1, 2, 3, 5, 8, 13, 22, 38, 66, 116, 205, 364, 649, 1159, 2073, 3712, 6650, 11919, 21370, 38322, 68732, 123287, 221158, 396744, 711760, 1276928, 2290904, 4110102, 7373977, 13229810, 23735985, 42585540, 76404334, 137080120, 245941268, 441254018, 791673612

Offset: 1

Author

Jonathan Vos Post, Feb 17 2010

Keywords

• easy
• nonn

Comments

Partial sums of number of partitions of 1 into n powers of 1/2. Partial sums of (according to one definition of "binary") the number of binary rooted trees. The subsequence of primes in this partial sum begins: 2, 3, 5, 13, a(43) = 26405436301.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000

Crossrefs

Partial sums of A002572.

Cf. A002573, A047913, A002574, A049284, A049285, A007178.

Formula

a(n) = Sum_{i=0..n} A002572(i).