cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Omar E. Pol, Aug 29 2011

Keywords

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.
		

Crossrefs

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.