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A151550 G.f.: Prod_{ n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)). 16
1, 1, 2, 1, 3, 4, 4, 1, 3, 4, 5, 5, 10, 12, 8, 1, 3, 4, 5, 5, 10, 12, 9, 5, 10, 13, 15, 20, 32, 32, 16, 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, 32, 1, 3, 4, 5, 5, 10, 12, 9, 5, 10, 13, 15, 20, 32, 32, 17, 5, 10, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

When convolved with [1, 2, 2, 2,...] gives the toothpick sequence A153006: (1, 3, 6, 9,...). [From Gary W. Adamson, May 25 2009]

This sequence and the Adamson's comment both are mentioned in the Applegate-Pol-Sloane article, see chapter 8 "generating functions". - Omar E. Pol, Sep 20 2011

REFERENCES

D. 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

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..16383

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, which is also available at arXiv:1004.3036v2

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

FORMULA

To get a nice recurrence, change the offset to 0 and multiply the g.f. by x as in the triangle in the example lines. Then we have: a(0)=0; a(2^i)=1; a(2^i-1)=2^(i-1) for i >= 1; otherwise write n = 2^i+j with 1 <= j <= 2^i-2, then a(n) = a(2^i+j) = 2*a(j) + a(j+1).

EXAMPLE

Contribution from Omar E. Pol, Jun 09 2009, edited by N. J. A. Sloane, Jun 17 2009:

May be written as a triangle:

.0;

.1;

.1,2;

.1,3,4,4;

.1,3,4,5,5,10,12,8;

.1,3,4,5,5,10,12,9,5,10,13,15,20,32,32,16;

.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,...

The rows of the triangle converge to A151555.

CROSSREFS

For generating functions of the form Prod_{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. A139250, A151551, A151552, A151553, A151554, A151555, A152980, A153006, A151688.

Cf. A000079. [From Omar E. Pol, Jun 09 2009]

Sequence in context: A002124 A097564 A128270 * A097003 A193788 A109447

Adjacent sequences:  A151547 A151548 A151549 * A151551 A151552 A151553

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 19 2009, Jun 17 2009

STATUS

approved

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Last modified May 30 04:27 EDT 2017. Contains 287305 sequences.