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

0,2

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.

Sequence in context: A081295 A180565 A233187 * A301786 A258411 A059743

Adjacent sequences: A160423 A160424 A160425 * A160427 A160428 A160429

Keyword

nonn

Author

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

Extensions

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

Status

approved