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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A171889 A171868 A292146 * A162784 A093660 A093663

Adjacent sequences:  A101907 A101908 A101909 * A101911 A101912 A101913

KEYWORD

eigen,nonn

AUTHOR

Paul D. Hanna, Dec 21 2004

STATUS

approved

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Last modified April 18 12:42 EDT 2019. Contains 322209 sequences. (Running on oeis4.)