

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

Also, total number of ON cells at stage n of the twodimensional cellular automaton defined as follows: replace every "vertical" toothpick of length 2 with a 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 the structure 45 degrees and then replace every toothpick with a unit square "ON" cell. For the illustration of the sequence as a cellular automaton we now have three versions: the original version with toothpicks, the onestep rook version and onestep bishop version. Note that the last two versions refer 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



FORMULA



EXAMPLE

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.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



