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A147582
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First differences of A147562.
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32
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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D. Singmaster, On the cellular automaton of Ulam and Warburton, unpublished manuscript, 2003.
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.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
David Applegate, The movie version
O. E. Pol, Illustration of initial terms (One-step rook) [From Omar E. Pol, Nov 02 2009]
O. E. Pol, Illustration of initial terms (One-step bishop) [From Omar E. Pol, Nov 02 2009]
O. E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol, Nov 02 2009]
O. E. Pol, Illustration of initial terms (Overlapping X-toothpicks) [From Omar E. Pol, Nov 12 2009]
O. E. Pol, Illustration of initial terms of A139251, A160121, A147582 (Overlapping figures) [From Omar E. Pol, Nov 12 2009]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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FORMULA
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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.
G.f.: x + 4*x*(Prod_{k>=0} (1+3*x^(2^k)) - 1)/3. - N. J. A. Sloane, Jun 10 2009
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EXAMPLE
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Contribution from Omar E. Pol, Jun 14 2009: (Start)
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)
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MAPLE
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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
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CROSSREFS
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Cf. A147562, A147610 (the sequence divided by 4), A048881.
Cf. A000079, A161411, A151779, A139250.
Cf. A048883, A139251, A160121, A162349. [From Omar E. Pol, Nov 02 2009]
Sequence in context: A178182 A160721 A151836 * A162793 A169708 A109045
Adjacent sequences: A147579 A147580 A147581 * A147583 A147584 A147585
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 29 2009
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EXTENSIONS
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Extended by R. J. Mathar, Apr 30 2009
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STATUS
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approved
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