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A160721 First differences of A160720.

%I A160721 #17 Feb 24 2021 02:48:18
%S A160721 1,4,4,12,4,12,12,28,4,12,12,28,12,28,28,60,4,12,12,28,12,28,28,60,12,
%T A160721 28,28,60,28,60,60,124,4,12,12,28,12,28,28,60,12,28,28,60,28,60,60,
%U A160721 124,12,28,28,60,28,60,60,124,28,60,60,124,60,124,124,252,4,12,12,28,12,28,28
%N A160721 First differences of A160720.
%C A160721 This sequence is related to the Sierpinski triangle and to Gould's sequence A001316. - _Omar E. Pol_, Jul 23 2009
%C A160721 When written as a irregular triangle in which row lengths are A011782 it appears that right border gives A173033. - _Omar E. Pol_, Mar 20 2013
%H A160721 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 A160721 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A160721 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>
%H A160721 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A160721 a(1)=1. Observation: It appears that a(n) = 4*A038573(n-1), n>1. [From _Omar E. Pol_, Jul 23 2009]. This formula is correct! - _N. J. A. Sloane_, Jan 23 2016
%e A160721 From _Omar E. Pol_, Mar 20 2013 (Start):
%e A160721 Triangle begins:
%e A160721 1;
%e A160721 4;
%e A160721 4,12;
%e A160721 4,12,12,28;
%e A160721 4,12,12,28,12,28,28,60;
%e A160721 4,12,12,28,12,28,28,60,12,28,28,60,28,60,60,124;
%e A160721 4,12,12,28,12,28,28,60,12,28,28,60,28,60,60,124,12,28,28,60,28,60,60,124,28,60,60,124,60,124,124,252;
%e A160721 (End)
%Y A160721 Cf. A000120, A001316, A038573, A139250, A139251, A160720, A160722, A160723.
%K A160721 nonn,tabf
%O A160721 1,2
%A A160721 _Omar E. Pol_, May 25 2009, May 29 2009
%E A160721 More terms from _R. J. Mathar_, Jul 14 2009