A160430 The 3-D toothpick sequence A160160, but using toothpicks of length 4; a(n) is the number of nodes occupied after n steps.

0, 5, 13, 29, 57, 85, 113, 145, 209, 329, 509, 613, 665, 697, 761, 881, 1073, 1273, 1505, 1817, 2377, 3217, 4309, 4761, 4921, 5009, 5097, 5233, 5425, 5625, 5857, 6169, 6729, 7569, 8697, 9425, 10017, 10641, 11601, 12873

Offset

0,2

Links

Table of n, a(n) for n=0..39.

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

Formula

a(n) = A170884(n) + 2*A160160(n)

Example

Each toothpick looks like this: o-o-o-o-o.
The initial (z-axis) toothpick occupies 5 nodes. The next two, in the x-direction, add 8 further nodes, and so on.

Crossrefs

Cf. A139250, A139251, A147562, A160118, A160120, A160160, A160170, A160379, A160420.

Sequence in context: A307674 A273026 A273077 * A347503 A023617 A023619

Adjacent sequences: A160427 A160428 A160429 * A160431 A160432 A160433

Keyword

nonn

Author

Omar E. Pol, May 13 2009

Extensions

Edited by N. J. A. Sloane, Jan 02 2010

Formula and more terms from Nathaniel Johnston, Nov 14 2010

Status

approved