login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A180714 Sum of the x- and y-coordinates of a point moving in a clockwise spiral. 2
0, 1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A spiral on the simple square grid is constructed starting at (0,0) and walking in the closest self-avoiding clockwise loop: up 1 unit, right 1 unit, down 2 units, left 2 units, up 3 units etc. The step widths in the x coordinate are 0, 1, 0, -2, 0, 3,.. a signed version of A142150; the step widths in the y coordinate are 1, 0, -2, 0, 3,... The x coordinate after n steps (n>=0) is a signed variant of A002265(n+3), namely 0, 0, 1, 1, -1, -1, 2, 2, -2, -2, 3, ..; the y coordinate after n steps is 0, 1, 1, -1, -1, 2, 2, ... (n>=0). The sum of the x and y coordinate after n steps (at corners of the spiral) is c(n) = 0, 1, 2, 0, -2, 1, 4, 0, -4, 1, 6, 0, -6, 1, 8, 0,... with g.f. -x*(1+x)/( (x-1)*(x^2+1)^2). The current sequence is obtained by recording the sum of the two coordinates at all intermediate positions walking with a stride of 1 along the edges of the spiral, equivalent to showing all interpolating integers between two values of c(n). The first differences a(n+1)-a(n) are two 1's, four -1's, six 1's, eight -1's etc, blocks of +1 and -1 with run lengths increasing by 2. - R. J. Mathar, Jan 22 2011

LINKS

Peter Kagey, Table of n, a(n) for n = 0..10000

Image of the spiral

EXAMPLE

Spiral begins at x=0,y=0, then movers up-right-down-left-up-right-...

a(0)=0+0=0, a(1)=1+0=1, a(2)=1+1=2, a(3)=0+1=1, a(4)=-1+1=0, a(5)=-1+0=-1, ...

CROSSREFS

Cf. A065358, A174344.

Sequence in context: A065368 A010751 A194523 * A170959 A170960 A170961

Adjacent sequences:  A180711 A180712 A180713 * A180715 A180716 A180717

KEYWORD

sign

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 21 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 05:18 EST 2016. Contains 278773 sequences.