A101910 A fractal sequence such that a(n) = A101911(A000120(n-1)) for n>0, where A101911 is the binomial transform of this sequence.

1, 1, 2, 2, 5, 2, 5, 5, 12, 2, 5, 5, 12, 5, 12, 12, 30, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30, 30, 73, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30, 30, 73, 5, 12, 12, 30, 12, 30, 30, 73, 12, 30, 30, 73, 30, 73, 73, 169, 2, 5, 5, 12, 5, 12, 12, 30, 5, 12, 12, 30, 12, 30

Offset

0,3

Comments

A101911 also forms the records in this sequence at positions 2^k for k>=0. A000120 is the binary 1's-counting sequence. Removing the even-indexed terms shifts this sequence one place left.

Links

Table of n, a(n) for n=0..78.

Formula

a(n) = Sum_{k=0, n-1} Mod(C(n-1, k), 2)*a(A000120(n-k-1)) for n>0, a(0)=1. a(2^k) = A101911(k) for k>=0.

Example

Denote the n-th term of the binomial transform by: b(n)=A101911(n):
A101911 = {1,2,5,12,30,73,169,377,831,1842,4110,...}.
Note A000120 = {0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,...}.
Then this sequence is formed by the following construct:
{1,b(0),b(1),b(1),b(2),b(1),b(2),b(2),b(3),...,b(A000120(n-1)),...}
so that a(2^0)=b(0), a(2^1)=b(1), a(2^2)=b(2), a(2^3)=b(3), ...

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, (binomial(n-1, k)%2)*a(subst(Pol(binary(n-k-1)), x, 1))))}

Crossrefs

Cf. A101911, A000120.

Sequence in context: A292146 A334685 A340694 * A162784 A093660 A093663

Adjacent sequences: A101907 A101908 A101909 * A101911 A101912 A101913

Keyword

eigen,nonn

Author

Paul D. Hanna, Dec 21 2004

Status

approved