A151555 - OEIS

A151555

G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).

1, 3, 4, 5, 5, 10, 12, 9, 5, 10, 13, 15, 20, 32, 32, 17, 5, 10, 13, 15, 20, 32, 33, 23, 20, 33, 41, 50, 72, 96, 80, 33, 5, 10, 13, 15, 20, 32, 33, 23, 20, 33, 41, 50, 72, 96, 81, 39, 20, 33, 41, 50, 72, 97, 89, 66, 73, 107, 132, 172, 240, 272, 192, 65, 5, 10, 13, 15, 20, 32, 33, 23

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OFFSET

0,2

COMMENTS

From Gary W. Adamson, May 25 2009: (Start)

Convolved with A078008 signed (A151575) [1, 0, 2, -2, 6, -10, 22, -42, 86, -170, ...]

equals the toothpick sequence A153006: (1, 3, 6, 9, 13, 20, 28, ...). (End)

If A151550 is written as a triangle then the rows converge to this sequence. - N. J. A. Sloane, Jun 16 2009

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..16384

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

EXAMPLE

From Omar E. Pol, Jun 19 2009: (Start)

May be written as a triangle:

4,5;

5,10,12,9;

5,10,13,15,20,32,32,17;

5,10,13,15,20,32,33,23,20,33,41,50,72,96,80,33;

5,10,13,15,20,32,33,23,20,33,41,50,72,96,81,39,20,33,41,50,72,97,89,66,73,...

(End)

CROSSREFS

Cf. A139250, A151551, A151552, A151553, A151554, A151550, A152980, A153006.