

A160406


Toothpick sequence starting at the vertex of an infinite 90degree wedge.


32



0, 1, 2, 4, 6, 8, 10, 14, 18, 20, 22, 26, 30, 34, 40, 50, 58, 60, 62, 66, 70, 74, 80, 90, 98, 102, 108, 118, 128, 140, 160, 186, 202, 204, 206, 210, 214, 218, 224, 234, 242, 246, 252, 262, 272, 284, 304, 330, 346, 350, 356, 366, 376, 388, 408, 434, 452, 464, 484, 512, 542, 584
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OFFSET

0,3


COMMENTS

Consider the wedge of the plane defined by points (x,y) with y >= x, with the initial toothpick extending from (0,0) to (0,2); then extend by the same rule as for A139250, always staying inside the wedge.
Number of toothpick in the structure after n rounds.
The toothpick sequence A139250 is the main entry for this sequence. See also A153000. First differences: A160407.


LINKS



FORMULA

Let G = (x + 2*x^2 + 4*x^2*(1+x)*((Product_{k>=1} (1 + x^(2^k1) + 2*x^(2^k)))  1)/(1+2*x))/(1x) (= g.f. for A139250); then the g.f. for the present sequence is (G + 2 + x*(5x)/(1x)^2)*x/(2*(1+x)).  N. J. A. Sloane, May 25 2009


MAPLE

G := (x + 2*x^2 + 4*x^2*(1+x)*(mul(1+x^(2^k1)+2*x^(2^k), k=1..20)1)/(1+2*x))/(1x); P:=(G + 2 + x*(5x)/(1x)^2)*x/(2*(1+x)); series(P, x, 200); seriestolist(%); # N. J. A. Sloane, May 25 2009


MATHEMATICA

terms = 62;
G = (x + 2x^2 + 4x^2 (1+x)(Product[1+x^(2^k1) + 2x^(2^k), {k, 1, Ceiling[ Log[2, terms]]}]1)/(1+2x))/(1x);
P = (G + 2 + x(5x)/(1x)^2) x/(2(1+x));


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



