A160422 - OEIS

A160422

Number of "ON" cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the toothpick structure of A139250 but with toothpicks of length 6.

0, 7, 19, 41, 63, 87, 131, 193, 235, 259, 303, 367, 435, 527, 675, 837, 919, 943, 987, 1051, 1119, 1211, 1359, 1523, 1631, 1723, 1875, 2071, 2299, 2631, 3087, 3489, 3651, 3675, 3719, 3783, 3851, 3943, 4091, 4255, 4363, 4455, 4607, 4803, 5031, 5363, 5819, 6223, 6411

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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 6.

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

a(n) = A147614(n)+4*A139250(n) = A160420(n)+2*A139250(n) since each toothpick covers exactly four more grid points than the corresponding toothpick in A147614.

CROSSREFS

Cf. A139250, A139251, A147614, A160118, A160120, A160170, A160420, A160430.

Sequence in context: A191066 A087762 A195349 * A213782 A269428 A097240

Adjacent sequences: A160419 A160420 A160421 * A160423 A160424 A160425

KEYWORD

nonn

AUTHOR

Omar E. Pol, May 20 2009

EXTENSIONS

More terms and formula from Nathaniel Johnston, Nov 13 2010

STATUS

approved