OFFSET
0,6
LINKS
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
FORMULA
a(n) = (3^A151902(n)-1)/2.
MAPLE
f := proc(n) local j; j:=n mod 6; if (j<=1) then 0 elif (j<=4) then 1 else 2; fi; end;
wt := 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;
A151904 := proc(n) local k, j; k:=floor(n/6); j:=n-6*k; (3^(wt(k)+f(j))-1)/2; end;
MATHEMATICA
wt[n_] := DigitCount[n, 2, 1];
f[n_] := {0, 0, 1, 1, 1, 2}[[Mod[n, 6] + 1]];
A151902[n_] := wt[Floor[n/6]] + f[n - 6 Floor[n/6]];
a[n_] := (3^A151902[n] - 1)/2;
Table[a[n], {n, 0, 82}] (* Jean-François Alcover, Feb 16 2023 *)
PROG
(PARI) a(n)=(3^(hammingweight(n\6)+[0, 0, 1, 1, 1, 2][n%6+1])-1)/2 \\ Charles R Greathouse IV, Sep 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 31 2009
STATUS
approved