A170863 a(0) = 1, a(1) = 1; a(2^i + j) = 3a(j) + a(j + 1) for 0 <= j < 2^i.

1, 1, 4, 7, 4, 7, 19, 25, 4, 7, 19, 25, 19, 40, 82, 79, 4, 7, 19, 25, 19, 40, 82, 79, 19, 40, 82, 94, 97, 202, 325, 241, 4, 7, 19, 25, 19, 40, 82, 79, 19, 40, 82, 94, 97, 202, 325, 241, 19, 40, 82, 94, 97, 202, 325, 256, 97, 202, 340, 379, 493, 931, 1216, 727, 4, 7, 19, 25, 19, 40

Offset

0,3

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);
  3*procname(j) + procname(j+1)
end proc:
f(0):= 1: f(1):= 1:
map(f, [$0..100]); # Robert Israel, Jul 10 2020

Mathematica

f[n_] := f[n] = With[{j = n - 2^Floor@Log[2, n]}, 3 f[j] + f[j+1]];
f[0] = f[1] = 1;
f /@ Range[0, 100] (* Jean-François Alcover, Aug 31 2020, after Robert Israel *)

Crossrefs

Sequence in context: A081884 A059143 A094765 * A021682 A242187 A094692

Adjacent sequences: A170860 A170861 A170862 * A170864 A170865 A170866

Keyword

nonn,look

Author

N. J. A. Sloane, Jan 02 2010

Status

approved