

A147582


First differences of A147562.


54



1, 4, 4, 12, 4, 12, 12, 36, 4, 12, 12, 36, 12, 36, 36, 108, 4, 12, 12, 36, 12, 36, 36, 108, 12, 36, 36, 108, 36, 108, 108, 324, 4, 12, 12, 36, 12, 36, 36, 108, 12, 36, 36, 108, 36, 108, 108, 324, 12, 36, 36, 108, 36, 108, 108, 324, 36, 108, 108, 324, 108, 324, 324, 972, 4
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OFFSET

1,2


COMMENTS



REFERENCES

D. Singmaster, On the cellular automaton of Ulam and Warburton, M500 Magazine of the Open University, #195 (December 2003), pp. 27.
S. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962.


LINKS



FORMULA

a(1) = 1; for n > 1, a(n) = 4*3^(wt(n1)1) where wt() = A000120().  R. J. Mathar, Apr 30 2009
This formula is (essentially) given by Singmaster.  N. J. A. Sloane, Aug 06 2009
G.f.: x + 4*x*(Product_{k >= 0} (1 + 3*x^(2^k))  1)/3.  N. J. A. Sloane, Jun 10 2009


EXAMPLE

When written as a triangle:
.1;
.4;
.4,12;
.4,12,12,36;
.4,12,12,36,12,36,36,108;
.4,12,12,36,12,36,36,108,12,36,36,108,36,108,108,324;
.4,12,12,36,12,36,36,108,12,36,36,108,36,108,108,324,12,36,36,108,36,108,...
The rows converge to A161411. (End)


MAPLE

A000120 := proc(n) local w, m, i; w := 0; m := n; while m > 0 do i := m mod 2; w := w+i; m := (mi)/2; od; w; end: wt := A000120; A147582 := n> if n <= 1 then n else 4*3^(wt(n1)1); fi; [seq(A147582(n), n=0..1000)]; # N. J. A. Sloane, Apr 07 2010


MATHEMATICA

s = Plus @@ Flatten@ # & /@ CellularAutomaton[{686, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, 200]; f[n_] = If[n == 0, 1, s[[n + 1]]  s[[n]]]; Array[f, 120, 0] (* Michael De Vlieger, Apr 09 2015, after Nadia Heninger and N. J. A. Sloane at A147562 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



