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A161415 First differences of A160414. 8
1, 8, 12, 28, 12, 36, 36, 92, 12, 36, 36, 108, 36, 108, 108, 292, 12, 36, 36, 108, 36, 108, 108, 324, 36, 108, 108, 324, 108, 324, 324, 908, 12, 36, 36, 108, 36, 108, 108, 324, 36, 108, 108, 324, 108, 324, 324, 972, 36, 108, 108, 324, 108, 324, 324, 972, 108, 324, 324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

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

Omar E. Pol, Illustration of initial terms [From Omar E. Pol, Nov 11 2009]

D. Applegate, Omar E. Pol, N. J. A. Sloane, The toothpick sequence and other sequences from cellular automata, arXiv:1004.3036 [math.CO] [From R. J. Mathar, Oct 16 2010]

FORMULA

For n > 1, a(n) = 4*A048883(n-1), except a(n) = 4*A048883(n-1) - 2n if n is a power of 2. - N. J. A. Sloane, Jul 13 2009

MAPLE

Contribution from R. J. Mathar, Oct 16 2010: (Start)

isA000079 := proc(n) if type(n, 'even') then nops(numtheory[factorset](n)) = 1 ; else false ; fi ; end proc:

A048883 := proc(n) 3^wt(n) ; end proc:

A161415 := proc(n) if n = 1 then 1; elif isA000079(n) then 4*A048883(n-1)-2*n ; else 4*A048883(n-1) ; end if; end proc: seq(A161415(n), n=1..90) ; (End)

MATHEMATICA

a[1] = 1; a[n_] := 4*3^DigitCount[n-1, 2, 1] - If[IntegerQ[Log[2, n]], 2n, 0];

Array[a, 60] (* Jean-Fran├žois Alcover, Nov 17 2017, after N. J. A. Sloane *)

CROSSREFS

Cf. A139250, A139251, A160411, A160413, A160414, A160417.

Cf. A160727.

Cf. A048883, A161411, A162349. [From Omar E. Pol, Nov 11 2009]

Sequence in context: A072327 A218558 A181735 * A256531 A117802 A083485

Adjacent sequences:  A161412 A161413 A161414 * A161416 A161417 A161418

KEYWORD

nonn

AUTHOR

Omar E. Pol, May 20 2009, Jun 13 2009

EXTENSIONS

More terms from R. J. Mathar, Oct 16 2010

STATUS

approved

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Last modified December 7 20:33 EST 2019. Contains 329849 sequences. (Running on oeis4.)