

A101910


A fractal sequence such that a(n) = A101911(A000120(n1)) 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
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OFFSET

0,3


COMMENTS

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


LINKS

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


FORMULA

a(n) = Sum_{k=0, n1} Mod(C(n1, k), 2)*a(A000120(nk1)) for n>0, a(0)=1. a(2^k) = A101911(k) for k>=0.


EXAMPLE

Denote the nth 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(n1)),...}
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, n1, (binomial(n1, k)%2)*a(subst(Pol(binary(nk1)), 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



