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A151905 a(0) = a(2) = 0, a(1) = 1; for n >= 3, n = 3*2^k+j, 0 <= j < 3*2^k, a(n) = A151904(j). 5
0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 4, 0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 4, 4, 13, 13, 13, 40, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Consider the Holladay-Ulam CA shown in Fig. 2 and Example 2 of the Ulam article. Then a(n) is the number of cells turned ON in generation n in a 45 degree sector that are not on the main stem.

REFERENCES

S. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962.

LINKS

Table of n, a(n) for n=0..90.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata

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

N. J. A. Sloane, Illustration of initial terms (annotated copy of figure on p. 222 of Ulam)

EXAMPLE

If written as a triangle:

0,

1, 0,

0, 0, 1,

0, 0, 1, 1, 1, 4,

0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13,

0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40

0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 4, 4, 13, 13, 13, 40, 13, 13, 40, 40, 40, 121,

...

then the rows converge to A151904.

MAPLE

f := proc(n) local j; j:=n mod 6; if (j<=1) then 0 elif (j<=4) then 1 else 2; fi; end;

wt := proc(n) local w, m, i; w := 0; m := n; while m > 0 do i := m mod 2; w := w+i; m := (m-i)/2; od; w; end;

A151904 := proc(n) local k, j; k:=floor(n/6); j:=n-6*k; (3^(wt(k)+f(j))-1)/2; end;

A151905 := proc (n) local k, j;

if (n=0) then 0;

elif (n=1) then 1;

elif (n=2) then 0;

else k:=floor( log(n/3)/log(2) ); j:=n-3*2^k; A151904(j); fi;

end;

CROSSREFS

Cf. A151904, A151906, A151907, A139250, A151895, A151896.

Sequence in context: A200627 A152889 A216273 * A226997 A078669 A229655

Adjacent sequences:  A151902 A151903 A151904 * A151906 A151907 A151908

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jul 31 2009

STATUS

approved

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Last modified April 25 03:02 EDT 2014. Contains 240991 sequences.