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

Author

Hans G. Oberlack, Oct 31 2015

Keywords

• nonn
• easy

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

• Hans G. Oberlack, Sketch of a block spiral

Crossrefs

Essentially the same as A008619.

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

Extensions

Edited by Wolfdieter Lang, Jan 05 2016