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 A151904 a(n) = (3^(wt(k)+f(j))-1)/2 if n = 6k+j, 0 <= j < 6, where wt = A000120, f = A151899. 6
 0, 0, 1, 1, 1, 4, 1, 1, 4, 4, 4, 13, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 4, 4, 13, 13, 13, 40, 13, 13, 40, 40, 40, 121, 1, 1, 4, 4, 4, 13, 4, 4, 13, 13, 13, 40, 4, 4, 13, 13, 13, 40, 13, 13, 40, 40, 40, 121, 4, 4, 13, 13, 13, 40, 13, 13, 40, 40, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Table of n, a(n) for n=0..82. 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 Cf, A151899, A151902, A151905-A151907. Sequence in context: A183374 A176263 A110812 * A356296 A222360 A222371 Adjacent sequences: A151901 A151902 A151903 * A151905 A151906 A151907 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jul 31 2009 STATUS approved

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Last modified August 12 15:11 EDT 2024. Contains 375113 sequences. (Running on oeis4.)