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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.)