A153004 First differences of toothpick numbers A153003.

1, 3, 3, 3, 6, 9, 6, 3, 6, 9, 9, 12, 21, 24, 12, 3, 6, 9, 9, 12, 21, 24, 15, 12, 21, 27, 30, 45, 66, 60, 24, 3, 6, 9, 9, 12, 21, 24, 15, 12, 21, 27, 30, 45, 66, 60, 27, 12, 21, 27, 30, 45, 66, 63, 42, 45, 69, 84, 105, 156, 192, 144, 48, 3

Offset

1,2

Links

Table of n, a(n) for n=1..64.

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

Example

Triangle begins:
1;
3,3;
3,6,9,6;
3,6,9,9,12,21,24,12;
3,6,9,9,12,21,24,15,12,21,27,30,45,66,60,24;

Mathematica

A139250[n_] := A139250[n] = Module[{m, k}, If[n == 0, Return[0]]; m = 2^(Length[IntegerDigits[n, 2]] - 1); k = (2 m^2 + 1)/3; If[n == m, k, k + 2 A139250[n - m] + A139250[n - m + 1] - 1]];
b[n_] := If[n == 0, 0, (3/4) (A139250[n + 1] - 3) + 1];
b /@ Range[0, 64] // Differences (* Jean-François Alcover, Apr 06 2020 *)

Crossrefs

Cf. A139251, A152968, A152978, A152998, A153000, A153003.

Toothpick sequence: A139250.

Sequence in context: A058675 A025497 A031502 * A214361 A124449 A262877

Adjacent sequences: A153001 A153002 A153003 * A153005 A153006 A153007

Keyword

nonn

Author

Omar E. Pol, Jan 02 2009

Status

approved