A160420 - OEIS

A160420

Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose skeleton is the same network as the toothpick structure of A139250 but with toothpicks of length 4.

0, 5, 13, 27, 41, 57, 85, 123, 149, 165, 193, 233, 277, 337, 429, 527, 577, 593, 621, 661, 705, 765, 857, 957, 1025, 1085, 1181, 1305, 1453, 1665, 1945, 2187, 2285, 2301, 2329, 2369, 2413, 2473, 2565, 2665, 2733, 2793, 2889, 3013, 3161, 3373, 3653, 3897, 4013

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OFFSET

0,2

COMMENTS

a(n) is also the number of grid points that are covered after n-th stage by an polyedge as the toothpick structure of A139250, but with toothpicks of length 4.

LINKS

Table of n, a(n) for n=0..48.

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.]

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

FORMULA

Conjecture: a(n) = A147614(n)+2*A139250(n). [From R. J. Mathar, Jan 22 2010]

The above conjecture is true: each toothpick covers exactly two more grid points than the corresponding toothpick in A147614.

EXAMPLE

a(2)=13:

.o-o-o-o-o

.....|....

.....o....

.....|....

.....o....

.....|....

.....o....

.....|....

.o-o-o-o-o

CROSSREFS

Cf. A139250, A139251, A147614, A147562, A160118, A160120, A160170, A160430.

Sequence in context: A211637 A256111 A322417 * A182840 A301675 A147411

Adjacent sequences: A160417 A160418 A160419 * A160421 A160422 A160423

KEYWORD

nonn

AUTHOR

Omar E. Pol, May 13 2009, May 18 2009

EXTENSIONS

Definition revised by N. J. A. Sloane, Jan 02 2010.

Formula verified and more terms from Nathaniel Johnston, Nov 13 2010

STATUS

approved