A160808 -id:A160808 - cp's OEIS frontend

A160809 First differences of A160808.

1, 2, 4, 4, 4, 8, 12, 4, 1, 2, 3, 3, 4, 7, 8, 1, 2, 3, 3, 4, 5, 7, 5, 3, 5, 7, 8, 11, 13, 17, 12, 4, 5, 8, 7, 9, 5, 7, 9, 8, 4, 8, 8, 7, 8, 13, 14, 10, 8, 12, 11, 13, 13, 17, 16, 11, 8, 15, 13, 14, 19, 26, 21, 5, 7

Offset: 1

Omar E. Pol, May 26 2009

nonn

Number of toothpicks added to the spiral at the n-th stage.

Nathaniel Johnston, Table of n, a(n) for n = 1..254
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. A000045, A139250, A139251, A160426, A160427, A160800, A160801, A160802, A160803, A160808.

Terms after a(16) from Nathaniel Johnston, Mar 30 2011

A160426 Toothpick sequence starting from an asymmetric cross, with four edges of length 1, 2, 3 and 4, formed by five toothpicks of length 2.

Original entry on oeis.org

0, 5, 9, 17, 30, 42, 52, 69, 90, 102, 112, 129, 150, 170, 196, 237, 274, 286, 296, 313, 334, 354, 380, 421, 458, 478, 504, 545, 590, 642, 724, 829, 898, 910, 920, 937, 958, 978, 1004, 1045, 1082, 1102, 1128, 1169, 1214

Offset: 0

Omar E. Pol, May 25 2009, May 29 2009

nonn

On the infinite square grid we start at stage 0 with no toothpicks. At stage 1 we place three consecutive toothpicks and two orthogonal toothpicks, as an asymetric cross with four edges of length 1, 2, 3, and 4, then a(1)=5. At stage 2 we place 4 toothpicks. And so on...

The sequence gives the number of toothpicks in the structure after n stages. A160427 (the first differences) gives the number added at the n-th stage. See A139250 for more information about toothpick sequences.

Nathaniel Johnston, Table of n, a(n) for n = 0..455
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
Nathaniel Johnston, C program for computing terms

Cf. A139250, A139251, A160740, A160800, A160802, A160808.

Terms after a(13) from Nathaniel Johnston, Mar 31 2011

cp's OEIS Frontend

A160809 First differences of A160808.

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