

A280026


Fill an infinite square array by following a spiral around the origin; in the nth cell, enter the number of earlier cells that can be seen from that cell.


4



0, 1, 2, 3, 3, 4, 4, 5, 6, 5, 6, 7, 6, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 15, 11, 12, 13, 14, 15, 16, 12, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 19, 14, 15, 16, 17, 18, 19, 20, 21, 15, 16, 17, 18, 19, 20, 21
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OFFSET

0,3


COMMENTS

The spiral track being used here is the same as in A274640, except that the starting cell here is numbered 0 (as in A274641).
"Can be seen from" means "are on the same row, column, diagonal, or antidiagonal as".
The entry in a cell gives the number of earlier cells that are occupied in any of the eight cardinal directions.  Robert G. Wilson v, Dec 25 2016
First occurrence of k = 0,1,2,3,...: 0, 1, 2, 3, 5, 7, 8, 11, 14, 15, 19, 23, 24, 29, 34, 35, 41, 47, 48, 55, 62, ...  Robert G. Wilson v, Dec 25 2016


LINKS

Lars Blomberg, Table of n, a(n) for n = 0..10000


FORMULA

Empirically: a(0)=0, a(n+1)=a(n)+d for n>0, when n=k^2 or n=k*(k+1) then d=2k, else d=1.


EXAMPLE

The central portion of the spiral is:
.
79876
 
8 332 7
   
9 4 01 6
  
10 4565

89101112 ...


MATHEMATICA

a[n_] := a[n  1] + If[ IntegerQ@ Sqrt@ n  IntegerQ@ Sqrt[4n +1], 2  Select[{Sqrt@ n, (Sqrt[4n +1] 1)/2}, IntegerQ][[1]], 1]; a[0] = 0; Array[a, 76, 0] (* Robert G. Wilson v, Dec 25 2016 *)


CROSSREFS

See A280027 for an additive version.
Cf. A274640, A274641, A278354.
See A279211, A279212 for versions that follow antidiagonals in just one quadrant.
Sequence in context: A218535 A306592 A319246 * A323080 A194806 A229790
Adjacent sequences: A280023 A280024 A280025 * A280027 A280028 A280029


KEYWORD

nonn,tabl


AUTHOR

N. J. A. Sloane, Dec 24 2016


EXTENSIONS

Corrected a(23) and more terms from Lars Blomberg, Dec 25 2016


STATUS

approved



