A106461 Binomial transform of the Tower of Hanoi sequence.

1, 3, 6, 13, 28, 58, 116, 229, 456, 924, 1896, 3898, 7960, 16084, 32168, 63845, 126160, 248968, 491952, 975388, 1943536, 3895336, 7852688, 15906874, 32321264, 65736728, 133549136, 270550228, 545928688, 1096685608, 2193371216, 4369711461, 8679052960

Offset: 1

Author

Gary W. Adamson, May 02 2005

Keywords

• nonn
• easy

Examples

			a(4) = 13 = 1*1 + 3*2 + 3*1 + 1*3, where the Tower of Hanoi sequence = (A001511): 1, 2, 1, 3, 1, 2, 1, 4...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3310

Crossrefs

Cf. A001511.

Programs

Maple

f:= n -> add(padic:-ordp(2*k,2)*binomial(n-1,k-1),k=1..n):
map(f, [$1..100]); # Robert Israel, Dec 02 2016

Formula

Binomial transform of A001511, the "ruler" or Tower of Hanoi sequence.

a(2^n-1) = 2*a(2^n-2) for n > 1. - A.H.M. Smeets, May 08 2019

Extensions

More terms from N. J. A. Sloane, May 03 2008