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A280026 Fill an infinite square array by following a spiral around the origin; in the n-th 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 (list; table; graph; refs; listen; history; text; internal format)
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=2-k, else d=1.

EXAMPLE

The central portion of the spiral is:

.

    7---9---8---7---6

    |               |

    8   3---3---2   7

    |   |       |   |

    9   4   0---1   6

    |   |           |

   10   4---5---6---5

    |

    8---9--10--11--12 ...

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

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)