A256537 - OEIS

%I #33 Nov 13 2024 23:02:55

%S 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 49,41,73,101,93,101,125,65,9,17,29,37,37,53,85,85,53,53,93,133,141,

%U 149,197,181,81,41,73,101,109,141,221,253,173,117,173,249,237,237,265,129

%N First differences of corner sequence A256536 associated with A151723.

%C 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 For an animation see "The movie version" in Links section.

%H David Applegate, <a href="/A139250/a139250.anim.html">The movie version</a>

%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>

%H <a href="/index/To#toothpick">Index entries for sequences related to toothpick sequences</a>

%F a(1) = 1; a(2) = 3.

%F It appears that a(n) = 1 + (A151724(n) + A151724(n-1))/3, n >= 3.

%F It appears that a(n) = 1 + (A151723(n) - A151723(n-2))/3, n >= 3.

%F It appears that a(n) = 1 + 2*(A170898(n-2) + A170898(n-3)), n >= 3.

%F a(3) = 5.

%F It appears that a(n) = 1 + 2*(A169779(n-2) - A169779(n-4)), n >= 4.

%e Written as an irregular triangle in which the row lengths are the absolute values of the terms of A141531, the sequence begins:

%e   1;

%e   3;

%e   5;

%e   9, 9;

%e   9, 17, 25, 17;

%e   9, 17, 29, 37, 33, 41, 57, 33;

%e   9, 17, 29, 37, 37, 53, 85, 85, 49, 41, 73, 101, 93, 101, 125, 65;

%e   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   ...

%e It appears that the right border gives A083318, whose representation in base 2 gives A000533.

%Y Cf. A000533, A083318, A141531, A151723, A151724, A169779, A170898, A256536.

%K nonn,tabf

%O 1,2

%A _Omar E. Pol_, Apr 02 2015