A194443 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194442.

0, 1, 2, 4, 4, 4, 4, 7, 8, 4, 4, 8, 12, 8, 8, 13, 16, 4, 4, 8, 12, 16, 16, 20, 24, 12, 8, 16, 28, 16, 16, 25, 32, 4, 4, 8, 12, 16, 16, 22, 32, 26, 20, 24, 40, 32, 40, 33, 48, 20, 8, 16, 28, 40, 44, 50, 60, 28, 16, 32, 60, 32, 32, 49, 64, 4, 4, 8

Offset: 0

Author

Omar E. Pol, Aug 29 2011

Keywords

• nonn

Comments

Essentially the first differences of A194442. It appears that the structure of the "narrow" triangle is much more regular about n=2^k, see formula section.

Examples

			If written as a triangle:
0,
1,
2,
4,4,
4,4,7,8,
4,4,8,12,8,8,13,16,
4,4,8,12,16,16,20,24,12,8,16,28,16,16,25,32,
4,4,8,12,16,16,22,32,26,20,24,40,32,40,33,48,20,8,16,28...
.
It appears that rows converge to A194697.
		

Links

• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

Cf. A139251, A160121, A160407, A161831, A194271, A194441, A194442, A194445, A194694, A194695, A194697.

Formula

Conjectures for n = 2^k+j, if -6<=j<=6:

a(2^k-6) = 2^(k-2), if k >= 3.

a(2^k-5) = 2^(k-1), if k >= 3.

a(2^k-4) = 2^k-4, if k >= 2.

a(2^k-3) = 2^(k-1), if k >= 3.

a(2^k-2) = 2^(k-1), if k >= 2.

a(2^k-1) = 3*2^(k-2)+1, if k >= 2.

a(2^k+0) = 2^k, if k >= 0.

a(2^k+1) = 4, if k >= 1.

a(2^k+2) = 4, if k >= 1.

a(2^k+3) = 8, if k >= 3.

a(2^k+4) = 12, if k >= 3.

a(2^k+5) = 16, if k >= 4.

a(2^k+6) = 16, if k >= 4.

End of conjectures.