A160128 a(n) = number of grid points that are covered after (2^n)th stage of A139250.

3, 7, 19, 63, 235, 919, 3651, 14575, 58267, 233031, 932083, 3728287, 14913099, 59652343, 238609315, 954437199, 3817748731, 15270994855, 61083979347, 244335917311, 977343669163, 3909374676567, 15637498706179

Offset

0,1

Links

Table of n, a(n) for n=0..22.

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

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

a(n) = A147614(A000079(n)).

a(n) = (1/9)*(2^(2*n+3) + 12*n + 19). [Nathaniel Johnston, Mar 29 2011]

It appears that a(n) = A139252(2^(n+1)). - Omar E. Pol, Sep 11 2012

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3). - Paul Curtz, May 07 2020

G.f.: (3 - 11*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)). - Colin Barker, May 13 2020

Prog

(PARI) Vec((3 - 11*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^40)) \\ Colin Barker, May 13 2020

Crossrefs

Cf. A000079, A007583, A139250, A139251, A139252, A139560, A147614.

Cf. Same recurrence: A073724, A210985, A014825.

Sequence in context: A249380 A364626 A210985 * A051139 A049423 A121825

Adjacent sequences: A160125 A160126 A160127 * A160129 A160130 A160131

Keyword

nonn,easy

Author

Omar E. Pol, May 09 2009

Extensions

Terms after a(10) from Nathaniel Johnston, Mar 29 2011

Status

approved