A170860 - OEIS

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A170860

a(0) = 1, a(1) = 0; a(2^i + j) = a(j) + 3a(j + 1) for 0 <= j < 2^i.

1, 0, 1, 3, 1, 3, 10, 6, 1, 3, 10, 6, 10, 33, 28, 9, 1, 3, 10, 6, 10, 33, 28, 9, 10, 33, 28, 36, 109, 117, 55, 12, 1, 3, 10, 6, 10, 33, 28, 9, 10, 33, 28, 36, 109, 117, 55, 12, 10, 33, 28, 36, 109, 117, 55, 39, 109, 117, 136, 363, 460, 282, 91, 15, 1, 3, 10, 6, 10, 33, 28, 9, 10, 33, 28, 36

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

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

MAPLE

f:= proc(n) option remember;

local j;

j:= n - 2^ilog2(n);

procname(j) + 3*procname(j+1)

end proc:

f(0):= 1: f(1):= 0:

map(f, [$0..100]); # Robert Israel, Jul 10 2020

MATHEMATICA

Nest[Append[#1, #1[[#2 + 1]] + 3 #1[[#2 + 2]]] & @@ {#1, #2 - 2^Floor@ Log2@ #2} & @@ {#, Length@ #} &, {1, 0}, 82] (* Michael De Vlieger, Jul 10 2020 *)

CROSSREFS

Sequence in context: A257253 A378377 A067329 * A170845 A375720 A025238

Adjacent sequences: A170857 A170858 A170859 * A170861 A170862 A170863

KEYWORD

nonn,look

AUTHOR

N. J. A. Sloane, Jan 02 2010

STATUS

approved