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A162777
a(n) = A153003(n) - A153006(n).
2
0, 0, 1, 1, 1, 3, 5, 3, 1, 3, 5, 5, 7, 13, 15, 7, 1, 3, 5, 5, 7, 13, 15, 9, 7, 13, 17, 19, 29, 43, 39, 15, 1, 3, 5, 5, 7, 13, 15, 9, 7, 13, 17, 19, 29, 43, 39, 17, 7, 13, 17, 19, 29, 43, 41, 27, 29, 45, 55, 69, 103, 127, 95, 31
OFFSET
0,6
COMMENTS
The main entry for this sequence is the toothpick sequence A139250.
LINKS
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
FORMULA
Observation: It appears that a(2^i) = 1, i > 0 and a(2^i-1) = 2^(i-1) - 1, i > 0.
EXAMPLE
If written as a triangle:
0;
0;
1,1;
1,3,5,3;
1,3,5,5,7,13,15,7;
1,3,5,5,7,13,15,9,7,13,17,19,29,43,39,15;
...
Rows converge to A162779.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jul 23 2009
EXTENSIONS
More terms from Jinyuan Wang, Mar 15 2020
STATUS
approved