A220499 Number of line segments in an H tree with n levels that have no correspondence with the toothpicks of the toothpick structure of A139250 after n-th stage.

0, 0, 0, 0, 4, 16, 40, 92, 212, 464, 968, 1980, 4016, 8096, 16260, 32612, 65364, 130896, 261960, 524092, 1048368, 2096928, 4194052, 8388324, 16776912, 33554112, 67108516, 134217344, 268435032, 536870428, 1073741252, 2147482996, 4294966612, 8589933904

Offset: 0

Author

Omar E. Pol, Feb 16 2013

Keywords

• nonn

Comments

More generally, differences between A000225 and A139250.

Examples

			For n = 0..3, the number of line segments in the H tree equals the number of toothpicks in the toothpick structure of A139250, so a(n) = 0, if 0 <= n <= 3. Note that there is a correspondence between every element from the two structures. For n = 4 the H tree contains 15 line segments, on the other hand the toothpick structure contains only 11 toothpicks. There are four line segments in the H tree that have no correspondence with the toothpicks of the toothpicks structure. They are the four line segments of the last generation that are closer to the center of the H tree, so a(4) = 4.
		

Links

• David Applegate, The movie version
• Brian Hayes, Joshua Trees and Toothpicks
• Brian Hayes, The Toothpick Sequence - Bit-Player
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Wikipedia, H tree
• Wikipedia, Toothpick sequence

Crossrefs

Cf. A000079, A000225, A139250, A139251, A152978, A152980, A153000, A153006.

Formula

a(n) = A000225(n) - A139250(n).