cp's OEIS Frontend

A160121 First differences of A160120.

%I A160121 #21 Feb 24 2021 02:48:18
%S A160121 1,3,3,9,3,9,9,21,9,9,9,21,15,21,27,51,27,9,9,21,15,21,27,51,33,21,27,
%T A160121 51,51,57,69,117,81,21,9,21,15,21,27,51,33,21,27,51,51,57,69,117,87,
%U A160121 33,27,51,51,57,75,129,117,75,69,117,135,141,171,279,231,69,9,21,15,21,27
%N A160121 First differences of A160120.
%C A160121 Number of Y-toothpicks added at n-th stage to the Y-toothpick structure of A160120.
%C A160121 For a simpler version, see A151710. - _Omar E. Pol_, Dec 18 2012
%H A160121 JungHwan Min, <a href="/A160121/b160121.txt">Table of n, a(n) for n = 1..5000</a>
%H A160121 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 A160121 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A160121 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polca002.jpg">Illustration of initial terms of A139251, A160121, A147582 (Overlapping figures)</a> [_Omar E. Pol_, Nov 02 2009]
%H A160121 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>
%e A160121 Contribution from _Omar E. Pol_, Jun 18 2009: (Start)
%e A160121 May be written as a triangle:
%e A160121 1,
%e A160121 3,
%e A160121 3,
%e A160121 9,
%e A160121 3,9,
%e A160121 9,21,9,9,
%e A160121 9,21,15,21,27,51,27,9,
%e A160121 9,21,15,21,27,51,33,21,27,51,51,57,69,117,81,21,
%e A160121 9,21,15,21,27,51,33,21,27,51,51,57,69,117,87,33,27,51,51,57,75,129,117,75,69,117,135,141,171,279,231,69;
%e A160121 Rows converge to A161326.
%e A160121 (End)
%e A160121 Contribution from _Omar E. Pol_, Dec 18 2012: (Start):
%e A160121 Also this sequence may be written as another triangle (according to the structure of triangle A151710):
%e A160121 1;
%e A160121 3;
%e A160121 3,  9;
%e A160121 3,  9,9,21;
%e A160121 9,  9,9,21,15,21,27,51;
%e A160121 27, 9,9,21,15,21,27,51,33,21,27,51,51,57,69,117;
%e A160121 81,21,9,21,15,21,27,51,33,21,27,51,51,57,69,117,87,33,27,51,51,57,75,129,117,75,69,117,135,141,171,279;
%e A160121 (End)
%t A160121 YTPFunc[lis_, step_] := With[{out = Extract[lis, {{1, 2}, {2, 1}, {-1, -1}}], in = lis[[2, 2]]}, Which[in == 1, 3, in == 0 && Count[out, 1] >= 2, 2, in == 0 && Count[out, 1] == 1, 1, True, in]]; A160121[n_] := Count[CellularAutomaton[{YTPFunc, {}, {1, 1}}, {{{1}}, 0}, {{{n}}}], 1, 2] (* _JungHwan Min_, Jan 28 2016 *)
%t A160121 A160121[n_] := Count[CellularAutomaton[{13390417258775213635414055181254541831894674613399006361662885886563211940509571858857491972104491013971547937418035084866785430974106432144737472376143620, 4, {{-1, 0}, {0, -1}, {0, 0}, {1, 1}}}, {{{1}}, 0}, {{{n}}}], 1, 2] (* _JungHwan Min_, Jan 28 2016 *)
%Y A160121 Cf. A139250, A139251, A151710, A160171, A160173, A160120, A160715, A161207, A161329, A161331, A161326, A161431, A147582.
%K A160121 nonn
%O A160121 1,2
%A A160121 _Omar E. Pol_, May 02 2009
%E A160121 More terms from _David Applegate_, Jun 14 2009