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

Author

Omar E. Pol, May 13 2009

Keywords

• nonn

Examples

			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.
		

Links

• 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

Crossrefs

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

Formula

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

Extensions

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

Formula and more terms from Nathaniel Johnston, Nov 14 2010