A139438 Frieze pattern with 5 rows, read by diagonals.

1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2

Offset

0,3

Comments

Period 15: repeat [1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1]. - Wesley Ivan Hurt, Jun 05 2016

Links

Table of n, a(n) for n=0..98.

James Propp, The combinatorics of frieze patterns and Markoff numbers, arXiv:math/0511633v4.

Formula

Four adjacent entries

...A...

.B...C.

...D...

satisfy D = (BC-1)/A.

Example

The frieze pattern is
... 1 1 1 1 1 1 1 ...
.....1 3 2 1 3 2 ...
....1 2 5 1 2 5 1 ...
.....1 3 2 1 3 2 ...
... 1 1 1 1 1 1 1 ...

Crossrefs

Cf. A139434, A139458.

Sequence in context: A141071 A004648 A265848 * A135392 A071947 A139343

Adjacent sequences: A139435 A139436 A139437 * A139439 A139440 A139441

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 09 2008

Status

approved