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%I #8 Feb 24 2021 02:48:18
%S 1,6,6,30,6,30,30,150,6,30,30,150,30,150,150,750,6,30,30,150,30,150,
%T 150,750,30,150,150,750,150,750,750,3750,6,30,30,150,30,150,150,750,
%U 30,150,150,750,150,750,750,3750,30,150,150,750,150,750,750,3750,150,750,750,3750
%N a(1)=1; for n > 1, a(n)=6*5^{wt(n-1)-1}.
%C Number of cells turned ON in n-th generation of cellular automaton based on Z^3 lattice in the same way that A147562 is based on the Z^2 lattice. Here each cell has six neighbors.
%H Charles R Greathouse IV, <a href="/A151779/b151779.txt">Table of n, a(n) for n = 1..10000</a>
%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, 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.]
%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>
%p 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:
%p f:=d->[seq((2*d)*(2*d-1)^(wt(n-1)-1),n=2..120)];
%p f2:=d->[1,op(f(d))];
%p f2(3);
%o (PARI) a(n)=6*5^(hammingweight(n-1)-1)\1 \\ _Charles R Greathouse IV_, Mar 07 2015
%Y Cf. A147582, A151780, A151781, A151782.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jun 25 2009
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