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

1,2

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.

Links

Table of n, a(n) for n=1..65.

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

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.

Example

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.

Crossrefs

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

Sequence in context: A292863 A377299 A160173 * A092996 A141264 A062949

Adjacent sequences: A256534 A256535 A256536 * A256538 A256539 A256540

Keyword

nonn,tabf

Author

Omar E. Pol, Apr 02 2015

Status

approved