

A162795


Total number of toothpicks in the toothpick structure A139250 that are parallel to the initial toothpick, after n odd rounds.


24



1, 5, 9, 21, 25, 37, 53, 85, 89, 101, 117, 149, 165, 201, 261, 341, 345, 357, 373, 405, 421, 457, 517, 597, 613, 649, 709, 793, 853, 965, 1173, 1365, 1369, 1381, 1397, 1429, 1445, 1481, 1541, 1621, 1637, 1673, 1733, 1817, 1877, 1989, 2197, 2389, 2405, 2441, 2501
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OFFSET

1,2


COMMENTS

Partial sums of A162793.
Also, total number of ON cells at stage n of twodimensional cellular automaton defined as follow: replace every "vertical" toothpick of length 2 with an centered unit square "ON" cell, so we have a cellular automaton which is similar to both A147562 and A169707 (this is the "onestep bishop" version). For the "onestep rook" version we use toothpicks of length sqrt(2), then rotate 45 degrees the structure and then replace every toothpick with a unit square "ON" cell. For the illustration of sequence as a cellular automaton now we have three versions: the original version with toothpicks, the onestep rook version and onestep bishop version. Note that the two last versions refers to the standard ON cells in the same way as the two versions of A147562 and the two versions of A169707. It appears that the graph of this sequence lies between the graphs of A147562 and A169707. Also, it appears that this sequence shares infinitely many terms with both A147562 and A169707, see Formula section and Example section.  Omar E. Pol, Feb 20 2015
It appears that this is also a bisection (the odd terms) of A255747.


LINKS

Michel Marcus, Table of n, a(n) for n = 1..10000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n1)1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS


FORMULA

It appears that a(n) = A147562(n) = A169707(n), if n is a member of A048645, otherwise A147562(n) < a(n) < A169707(n).  Omar E. Pol, Feb 20 2015
It appears that a(n) = (A169707(2n)  1)/4 = A255747(2n1).  Omar E. Pol, Mar 07 2015
a(n) = 1 + 4*A255737(n1).  Omar E. Pol, Mar 08 2015


EXAMPLE

From Omar E. Pol, Feb 18 2015: (Start)
Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782:
1;
5:
9, 21;
25, 37, 53, 85;
89, 101,117,149,165,201,261,341;
345,357,373,405,421,457,517,597,613,649,709,793,853,965,1173,1365;
...
The right border gives the positive terms of A002450.
(End)
It appears that T(j,k) = A147562(j,k) = A169707(j,k), if k is a power of 2, for example: it appears that the three mentioned triangles only share the elements of the columns 1, 2, 4, 8, 16, ...  Omar E. Pol, Feb 20 2015


CROSSREFS

Cf. A002450, A048645, A139250, A139251, A147562, A153000, A159791, A159792, A160164, A160552, A162793, A162794, A162796, A162797, A169707, A255263, A255264, A255747.
Sequence in context: A147552 A299776 A147562 * A255366 A269522 A169707
Adjacent sequences: A162792 A162793 A162794 * A162796 A162797 A162798


KEYWORD

nonn


AUTHOR

Omar E. Pol, Jul 14 2009


EXTENSIONS

More terms from N. J. A. Sloane, Dec 28 2009


STATUS

approved



