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%I
%S 1,4,4,12,4,12,12,36,4,12,12,36,12,36,36,108,4,12,12,36,12,36,36,108,
%T 12,36,36,108,36,108,108,324,4,12,12,36,12,36,36,108,12,36,36,108,36,
%U 108,108,324,12,36,36,108,36,108,108,324,36,108,108,324,108,324,324,972,4
%N First differences of A147562.
%D D. Singmaster, On the cellular automaton of Ulam and Warburton, unpublished manuscript, 2003.
%D 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.
%H N. J. A. Sloane, <a href="/A147582/b147582.txt">Table of n, a(n) for n = 1..10000</a>
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="http://neilsloane.com/doc/tooth.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>
%H David Applegate, <a href="http://www.research.att.com/~david/oeis/toothpick.html">The movie version</a>
%H O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca004.jpg">Illustration of initial terms (One-step rook)</a> [From _Omar E. Pol_, Nov 02 2009]
%H O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca006.jpg">Illustration of initial terms (One-step bishop)</a> [From _Omar E. Pol_, Nov 02 2009]
%H O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca008.jpg">Illustration of initial terms (Overlapping squares)</a> [From _Omar E. Pol_, Nov 02 2009]
%H O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca010.jpg">Illustration of initial terms (Overlapping X-toothpicks)</a> [From _Omar E. Pol_, Nov 12 2009]
%H O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca002.jpg">Illustration of initial terms of A139251, A160121, A147582 (Overlapping figures)</a> [From _Omar E. Pol_, Nov 12 2009]
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/toothlist.html">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%F a(1)=1; for n > 1, a(n)=4*3^{wt(n-1)-1}. - from _R. J. Mathar_, Apr 30 2009. This formula is (essentially) given by Singmaster - _N. J. A. Sloane_, Aug 06 2009.
%F G.f.: x + 4*x*(Prod_{k>=0} (1+3*x^(2^k)) - 1)/3. - _N. J. A. Sloane_, Jun 10 2009
%e Contribution from _Omar E. Pol_, Jun 14 2009: (Start)
%e When written as a triangle:
%e .1;
%e .4;
%e .4,12;
%e .4,12,12,36;
%e .4,12,12,36,12,36,36,108;
%e .4,12,12,36,12,36,36,108,12,36,36,108,36,108,108,324;
%e .4,12,12,36,12,36,36,108,12,36,36,108,36,108,108,324,12,36,36,108,36,108,...
%e The rows converge to A161411. (End)
%p A000120 := 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: wt := A000120; A147582 := n-> if n <= 1 then n else 4*3^(wt(n-1)-1); fi; [seq(A147582(n),n=0..1000)]; - _N. J. A. Sloane_, Apr 07 2010
%Y Cf. A147562, A147610 (the sequence divided by 4), A048881.
%Y Cf. A000079, A161411, A151779, A139250.
%Y Cf. A048883, A139251, A160121, A162349. [From _Omar E. Pol_, Nov 02 2009]
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Apr 29 2009
%E Extended by _R. J. Mathar_, Apr 30 2009
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