A188346 Number of hearts present in the n-th generation of the Q-toothpick sequence A187210.

0, 0, 0, 0, 0, 2, 4, 4, 4, 8, 12, 12, 12, 16, 20, 20, 28, 44, 52, 52, 52, 56, 60, 60, 68, 84, 92, 92, 96, 108, 116, 124, 156, 196, 212, 212, 212, 216, 220, 220, 228, 244, 252, 252, 256, 268, 276, 284, 316, 356, 372, 372, 376, 388, 396

Offset: 0

Author

Nathaniel Johnston, Mar 28 2011

Keywords

• nonn

Comments

See A187210 for a description of the different shapes that appear in the Q-toothpick sequence.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..181
• 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.]
• Nathaniel Johnston, The Q-Toothpick Cellular Automaton
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Crossrefs

Cf. A187210, A188344, A188345.

Formula

It appears that a(n) = A211008(n-2,2), n >= 3. (Checked by hand up n = 130 in the toothpick structure of A139250). - Omar E. Pol, Sep 25 2012