A161415 First differences of A160414.

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

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-François 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