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A256537 First differences of corner sequence A256536 associated with A151723.

%I A256537 #33 Nov 13 2024 23:02:55
%S A256537 1,3,5,9,9,9,17,25,17,9,17,29,37,33,41,57,33,9,17,29,37,37,53,85,85,
%T A256537 49,41,73,101,93,101,125,65,9,17,29,37,37,53,85,85,53,53,93,133,141,
%U A256537 149,197,181,81,41,73,101,109,141,221,253,173,117,173,249,237,237,265,129
%N A256537 First differences of corner sequence A256536 associated with A151723.
%C A256537 Number of cells turned ON at n-th stage in one of the outside corners of an infinite hexagon-shaped structure on hexagonal grid.
%C A256537 For an animation see "The movie version" in Links section.
%H A256537 David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>
%H A256537 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 A256537 <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>
%F A256537 a(1) = 1; a(2) = 3.
%F A256537 It appears that a(n) = 1 + (A151724(n) + A151724(n-1))/3, n >= 3.
%F A256537 It appears that a(n) = 1 + (A151723(n) - A151723(n-2))/3, n >= 3.
%F A256537 It appears that a(n) = 1 + 2*(A170898(n-2) + A170898(n-3)), n >= 3.
%F A256537 a(3) = 5.
%F A256537 It appears that a(n) = 1 + 2*(A169779(n-2) - A169779(n-4)), n >= 4.
%e A256537 Written as an irregular triangle in which the row lengths are the absolute values of the terms of A141531, the sequence begins:
%e A256537   1;
%e A256537   3;
%e A256537   5;
%e A256537   9, 9;
%e A256537   9, 17, 25, 17;
%e A256537   9, 17, 29, 37, 33, 41, 57, 33;
%e A256537   9, 17, 29, 37, 37, 53, 85, 85, 49, 41, 73, 101, 93, 101, 125, 65;
%e A256537   9, 17, 29, 37, 37, 53, 85, 85, 53, 53, 93, 133, 141, 149, 197, 181, 81, 41, 73, 101, 109, 141, 221, 253, 173, 117, 173, 249, 237, 237, 265, 129;
%e A256537   ...
%e A256537 It appears that the right border gives A083318, whose representation in base 2 gives A000533.
%Y A256537 Cf. A000533, A083318, A141531, A151723, A151724, A169779, A170898, A256536.
%K A256537 nonn,tabf
%O A256537 1,2
%A A256537 _Omar E. Pol_, Apr 02 2015