A151691 - OEIS

A151691

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

1, 2, 1, 2, 5, 4, 1, 2, 5, 4, 5, 12, 13, 6, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 5, 12, 13, 14, 29, 38, 25, 16, 29, 38, 41, 72, 105, 88, 41, 10, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 5, 12, 13, 14, 29

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..82.

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 09 2009: (Start)

Triangle begins:

2,1;

2,5,4,1;

2,5,4,5,12,13,6,1;

2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,1;

2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,38,41,72,...

(End)

CROSSREFS

For generating functions of the form Product_{k>=c} (1 + a*x^(2^k-1) + b*x^2^k) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694.

Cf. A151685. See A151703 for another version with a simpler recurrence.

Cf. A000079. - Omar E. Pol, Jun 09 2009

Sequence in context: A106480 A099602 A151703 * A201780 A337991 A104560

Adjacent sequences: A151688 A151689 A151690 * A151692 A151693 A151694

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 04 2009

STATUS

approved