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A147582 First differences of A147562. 32
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)
OFFSET

1,2

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

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

Omar E. Pol, Illustration of initial terms (One-step rook) [From Omar E. Pol, Nov 02 2009]

Omar E. Pol, Illustration of initial terms (One-step bishop) [From Omar E. Pol, Nov 02 2009]

Omar E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol, Nov 02 2009]

Omar E. Pol, Illustration of initial terms (Overlapping X-toothpicks) [From Omar E. Pol, Nov 12 2009]

Omar E. Pol, Illustration of initial terms of A139251, A160121, A147582 (Overlapping figures) [From Omar E. Pol, Nov 12 2009]

D. Singmaster, On the cellular automaton of Ulam and Warburton, Unpublished manuscript, 1973 [Cached copy, included with permission]

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

FORMULA

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

EXAMPLE

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)

MAPLE

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

CROSSREFS

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

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane, Apr 29 2009

EXTENSIONS

Extended by R. J. Mathar, Apr 30 2009

STATUS

approved

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Last modified July 24 22:06 EDT 2014. Contains 244897 sequences.