0,3

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.

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.

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

The three trisections are essentially A147582, A147582 and 3*A147582 respectively. More precisely, For t >= 1, a(3t) = a(3t+1) = A147582(t+1) = 4*3^(wt(t)-1), a(3t+2) = 4*A147582(t+1) = 4*3^wt(t). See A151907 for explanation.

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;

A151906 := proc(n);

if (n=0) then 0;

elif (n=1) then 1;

else 8*A151905(n) + 4;

fi;

end;

Cf. A151904, A151905, A151907, A139250, A151895, A151896.

Sequence in context: A117405 A013601 A035618 this_sequence A151896 A098525 A141666

Adjacent sequences: A151903 A151904 A151905 this_sequence A151907 A151908 A151909

nonn

David Applegate (david@research.att.com) and N. J. A. Sloane (njas(AT)research.att.com), Jul 31 2009, Aug 03 2009