A183127 Number of toothpicks added at n-th stage to the toothpick structure of A183126.

0, 1, 6, 16, 16, 40, 16, 40, 40, 112, 16, 40, 40, 112, 40, 112, 112, 328, 16, 40, 40, 112, 40, 112, 112, 328, 40, 112, 112, 328, 112, 328, 328, 976, 16, 40, 40, 112, 40, 112, 112, 328, 40, 112, 112, 328, 112, 328, 328, 976, 40, 112, 112, 328, 112, 328, 328, 976

Offset: 0

Author

Omar E. Pol, Mar 28 2011

Keywords

• nonn

Comments

Essentially the first differences of A183126.

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. A000120, A139250, A139251, A160173, A161411, A183126, A183149.

Programs

Mathematica

a[n_] := 4*(1 + 3^DigitCount[n-2, 2, 1]); a[0] = 0; a[1] = 1; a[2] = 6; Array[a, 100, 0] (* Amiram Eldar, Aug 01 2023 *)

Formula

a(n) = 4*(1 + 3^A000120(n-2)), n >= 3. - Nathaniel Johnston, Apr 06 2011

Extensions

a(0)-a(10) confirmed and a(11)-a(35) added by John W. Layman, Mar 30 2011

a(36)-a(47) from Nathaniel Johnston, Apr 06 2011

More terms from Amiram Eldar, Aug 01 2023