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A279211 Fill an array by antidiagonals upwards; in the n-th cell, enter the number of earlier cells that can be seen from that cell.

%I A279211 #39 Jul 14 2020 23:18:36
%S A279211 0,1,2,2,4,4,3,5,6,6,4,6,8,8,8,5,7,9,10,10,10,6,8,10,12,12,12,12,7,9,
%T A279211 11,13,14,14,14,14,8,10,12,14,16,16,16,16,16,9,11,13,15,17,18,18,18,
%U A279211 18,18,10,12,14,16,18,20,20,20,20,20,20,11,13,15,17
%N A279211 Fill an array by antidiagonals upwards; in the n-th cell, enter the number of earlier cells that can be seen from that cell.
%C A279211 "That can be seen from" means "that are on the same row, column, diagonal, or antidiagonal as".
%C A279211 Inspired by A279967.
%C A279211 Since the sum of row and column index is constant for elements in an antidiagonal, the entries along an antidiagonal on and above the diagonal equal twice the number of the antidiagonal. - _Hartmut F. W. Hoft_, Jun 29 2020
%H A279211 Alec Jones, <a href="/A279211/b279211.txt">Table of n, a(n) for n = 0..5049</a>
%F A279211 T(x,y) = x+3*y if x >= y; T(x,y) = 2*(x+y) if x <= y.
%F A279211 T(i, j) = i + 2*j + min(i, j). - _Hartmut F. W. Hoft_, Jun 29 2020
%e A279211 The array begins:
%e A279211 x\y| 0  1  2  3  4  5  6 ...
%e A279211 ---+--------------------
%e A279211   0| 0  2  4  6  8 10 12 ...
%e A279211   1| 1  4  6  8 10 12 ...
%e A279211   2| 2  5  8 10 12 ...
%e A279211   3| 3  6  9 12 ...
%e A279211   4| 4  7 10 13 ...
%e A279211   5| 5  8 11 14 ...
%e A279211   6| ...
%e A279211 ...
%e A279211 For example, when we get to the antidiagonal that reads 4, 6, 8 ..., the reason for the 8 is that from that cell we can see two cells that have been filled in above it (containing 4 and 6), two cells to the northwest (0, 4), two cells to the west (2, 5), and two to the southwest (4, 6), which is 8 cells, so a(12) = 8.
%t A279211 countCells[i_, j_] := i + 2*j + Min[i, j]
%t A279211 a279211[m_] := Map[countCells[m - #, #]&, Range[0, m]]
%t A279211 Flatten[Map[a279211,Range[0,10]]]  (* antidiagonals 0..10 data - _Hartmut F. W. Hoft_, Jun 29 2020 *)
%Y A279211 Cf. A279966, A279967, A279212.
%Y A279211 See A280026, A280027 for similar sequences based on a spiral.
%K A279211 nonn,tabl
%O A279211 0,3
%A A279211 _N. J. A. Sloane_, Dec 24 2016
%E A279211 More terms from _Alec Jones_, Dec 25 2016