A263997 Sequence of block lengths in a block spiral of width 1.

1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33

Offset

1,2

Comments

A left-handed block spiral is created by the following pattern: Start with a 1 X 1 square [ a(1)=1 ]. Attach a block of length 2 and width 1 (a horizontal 1 X 2 rectangle) to the upper side of the square [ a(2)=2 ] pointing to the right. Attach to the corner a vertical 2 X 1 block (rectangle). This block has length 2, so a(3)=2. Continue with a horizontal 1 X 2 block, so a(4) = 2. And so on. See the sketch shown in the link.

Links

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

Hans G. Oberlack, Sketch of a block spiral

Formula

a(n) = a(n-2) + 1 for n > 4.

O.g.f.: x*(1+x-x^2-x^3+x^4)/((1-x)*(1-x^2)). From A008619. - Wolfdieter Lang, Jan 05 2016

Crossrefs

Essentially the same as A008619.

Sequence in context: A112995 A368887 A078452 * A135636 A025795 A219610

Adjacent sequences: A263994 A263995 A263996 * A263998 A263999 A264000

Keyword

nonn,easy

Author

Hans G. Oberlack, Oct 31 2015

Extensions

Edited by Wolfdieter Lang, Jan 05 2016

Status

approved