A161418 -id:A161418 - cp's OEIS frontend

A161419 First differences of A161418.

Original entry on oeis.org

0, 0, 0, 6, 0, 6, 0, 12, 6

Offset: 1

Omar E. Pol, Jun 21 2009

Cf. A160120, A161418, A161829, A161837.

A161422 a(n) = A161418(n)/6.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 2, 4, 5

Offset: 0

Omar E. Pol, Jun 21 2009

Cf. A160120, A161418, A161834, A161838.

A161828 Number of rhombuses in the Y-toothpick structure of A160120 after n rounds.

Original entry on oeis.org

0, 0, 3, 3, 9, 9, 15, 21, 33, 39

Offset: 0

Omar E. Pol, Jun 21 2009

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, A160120, A160124, A161419, A161418, A161836.

A161836 Number of concave-convex hexagons in the Y-toothpick structure of A160120 after n rounds.

Original entry on oeis.org

0, 0, 0, 0, 3, 3, 3, 3, 9, 15

Offset: 0

Omar E. Pol, Jun 21 2009

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, A160120, A160124, A161419, A161418, A161828, A161837.

A194278 Total number of polygons after n-th stage in the D-toothpick structure of A194270.

Original entry on oeis.org

0, 0, 0, 0, 2, 8, 14, 16, 26, 38, 46, 48, 56, 72, 102

Offset: 0

Omar E. Pol, Aug 26 2011

The structure of the D-toothpick cellular automaton contains at least several tens of different types of polygons. For more information see A194276 and A194277.

			Consider the structure with toothpicks of length 2 and D-toothpicks of length sqrt(2). After 3 stages the number of polygons in the structure is equal to 0. After 4 stages there are 2 hexagons, each with area = 6, so a(4) = 2. After 5 stages there are new 6 polygons: 2 hexagons, each with area = 8 and also 2 octagons, each with area = 14, so a(5) = 2+6 = 8.

Cf. A160124, A170926, A161418, A161828, A161836, A194270, A194276, A194277.

cp's OEIS Frontend

A161419 First differences of A161418.

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A161422 a(n) = A161418(n)/6.

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A161828 Number of rhombuses in the Y-toothpick structure of A160120 after n rounds.

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A161836 Number of concave-convex hexagons in the Y-toothpick structure of A160120 after n rounds.

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A194278 Total number of polygons after n-th stage in the D-toothpick structure of A194270.

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