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

1,2

Links

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

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

Example

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...

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

Crossrefs

Cf. A001511.

Sequence in context: A103788 A371564 A182137 * A348124 A095768 A002478

Adjacent sequences: A106458 A106459 A106460 * A106462 A106463 A106464

Keyword

nonn,easy

Author

Gary W. Adamson, May 02 2005

Extensions

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

Status

approved