

A334812


a(0) = 0; a(1) = 1; for n > 1, a(n) is the square spiral number obtained from the magnitude of the difference between adjacent horizontal and vertical previously visited square numbers. If only one such adjacent square exists then it takes on that square's number.


1



0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1
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OFFSET

0


COMMENTS

As all squares are numbered from the difference between square spiral numbers which are either 0 or 1, all terms in the sequence are 0 or 1.
Inspired by Pascal's Spiral A334742.


LINKS

Table of n, a(n) for n=0..88.
Scott R. Shannon, Image of the spiral for a 101x101 grid. Black squares = 0 and white squares = 1, The central square a(0) = 0 is shown in red for clarity.
Scott R. Shannon, Image of the spiral for a 2001x2001 grid.


EXAMPLE

The spiral begins:
.
010011

11010 1
  
0 111 0 1
    
1 1 01 1 1
   
0 1100 0
 
010000
.
a(0) = 0; a(1) = 1 by definition.
a(2) = 1 as it only has one adjacent visited square a(1) = 1 so it takes that number.
a(3) = 1 as it has adjacent visited squares a(2) = 1 and a(0) = 0 and the difference between 1 and 0 is 1.
a(7) = 1 as it has adjacent visited squares a(6) = 1 and a(0) = 0 and the difference between 1 and 0 is 1.
a(8) = 0 as it has adjacent visited squares a(7) = 1 and a(1) = 1 and the difference between 1 and 1 is 0.
a(9) = 0 as it only has one adjacent visited square a(8) = 0 so it takes that number.


CROSSREFS

Cf. A334742, A174344, A274923, A274640, A328794.
Sequence in context: A175629 A109720 A022932 * A079421 A304438 A168181
Adjacent sequences: A334809 A334810 A334811 * A334813 A334814 A334815


KEYWORD

nonn


AUTHOR

Scott R. Shannon, May 12 2020


STATUS

approved



