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
Links
- 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).
Crossrefs
Programs
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PARI
Vec((3 - 11*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^40)) \\ Colin Barker, May 13 2020
Formula
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
Extensions
Terms after a(10) from Nathaniel Johnston, Mar 29 2011