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

0,3

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.

Links

Table of n, a(n) for n=0..67.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to toothpick sequences

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.

Example

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.

Crossrefs

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

Sequence in context: A063440 A008497 A220497 * A220523 A220527 A183226

Adjacent sequences: A194440 A194441 A194442 * A194444 A194445 A194446

Keyword

nonn

Author

Omar E. Pol, Aug 29 2011

Status

approved