A147614 -id:A147614 - cp's OEIS frontend

A194800 Number of grid points that are covered after n-th stage of A139250, assuming the vertical toothpicks have length 2 and the horizontal toothpicks have length 4.

0, 3, 11, 17, 31, 39, 67

Offset: 0

Omar E. Pol, Sep 07 2011

There are an infinite family of these sequences since A139250 gives the number of toothpicks in the structure regardless of the length difference between horizontal toothpicks and vertical toothpicks. Examples: A147614, this sequence, A194802, A160420, etc.

			a(2) = 11.
o o o o o
. . o . .
o o o o o

Cf. A139250, A147614, A162795, A162796, A162797, A175098, A160420, A160422, A194802.

A194802 Number of grid points that are covered after n-th stage of A139250, assuming the vertical toothpicks have length 4 and the horizontal toothpicks have length 2.

Original entry on oeis.org

0, 5, 9, 23, 29, 45, 57

Offset: 0

Omar E. Pol, Sep 07 2011

There are an infinite family of these sequences since A139250 gives the number of toothpicks in the structure regardless of the length difference between horizontal toothpicks and vertical toothpicks. Examples: A147614, A194800, this sequence, A160420, etc.

			a(2) = 9.
o o o
. o .
. o .
. o .
o o o

Cf. A139250, A147614, A162795, A162796, A162797, A175098, A160420, A160422, A194800

A162627 a(n) = A162625(n+1)/2.

Original entry on oeis.org

2, 3, 3, 4, 6, 7, 5, 4, 6, 8, 10, 14, 18, 17, 9, 4, 6, 8, 10, 14, 18, 18, 14, 14, 20, 26, 34, 46, 52, 41, 17, 4, 6, 8, 10, 14, 18, 18, 14, 14, 20, 26, 34, 46, 52, 42, 22, 14, 20, 26, 34, 46, 54, 50, 42, 48, 66, 86, 114, 144, 144, 97, 33, 4, 6, 8, 10, 14, 18, 18

Offset: 1

Omar E. Pol, Aug 05 2009

nonn

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.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A139250, A139251, A147614, A152968, A160421, A160423, A162625.

More terms from Jinyuan Wang, Mar 03 2020

A210985 Number of segments needed to draw the toothpick structure of A139250 as it is after 2^n stages.

Original entry on oeis.org

1, 3, 7, 19, 63, 235, 919, 3651, 14575

Offset: 0

Omar E. Pol, Sep 11 2012

It appears that this is also the partial sums of A039301.

It appears that this is also 1 together with A160128.

			For n = 3, after 2^3 stages the toothpick structure of A139250 contains 43 toothpicks (A139250(2^3) = 43). However the toothpick structure can be essentially represented by 19 segments (A139252(2^3) = 19), so a(3) = 19.

David Applegate, The movie version
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Cf. A007583, A039301, A139250, A139252, A147614, A160128.

a(n) = A139252(2^n).

cp's OEIS Frontend

A194800 Number of grid points that are covered after n-th stage of A139250, assuming the vertical toothpicks have length 2 and the horizontal toothpicks have length 4.

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A194802 Number of grid points that are covered after n-th stage of A139250, assuming the vertical toothpicks have length 4 and the horizontal toothpicks have length 2.

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A162627 a(n) = A162625(n+1)/2.

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A210985 Number of segments needed to draw the toothpick structure of A139250 as it is after 2^n stages.

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