A256537 First differences of corner sequence A256536 associated with A151723.

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, 49, 41, 73, 101, 93, 101, 125, 65, 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

Offset: 1

Author

Omar E. Pol, Apr 02 2015

Keywords

• nonn
• tabf

Comments

Number of cells turned ON at n-th stage in one of the outside corners of an infinite hexagon-shaped structure on hexagonal grid.

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

Examples

			Written as an irregular triangle in which the row lengths are the absolute values of the terms of A141531, the sequence begins:
  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, 49, 41, 73, 101, 93, 101, 125, 65;
  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;
  ...
It appears that the right border gives A083318, whose representation in base 2 gives A000533.
		

Links

• David Applegate, The movie version
• N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
• Index entries for sequences related to toothpick sequences

Crossrefs

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

Formula

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

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

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

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

a(3) = 5.

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