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.

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

Author

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

Keywords

• nonn

Comments

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.

Links

• 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

Crossrefs

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

Extensions

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