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A332529 Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.

%I A332529 #9 Jun 14 2022 19:33:17
%S A332529 0,2,1,5,3,2,7,6,4,3,10,8,7,5,4,13,11,9,8,6,5,15,14,12,10,9,7,6,18,16,
%T A332529 15,13,11,10,8,7,20,19,17,16,14,12,11,9,8,23,21,20,18,17,15,13,12,10,
%U A332529 9,26,24,22,21,19,18,16,14,13,11,10,28,27,25,23,22
%N A332529 Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
%C A332529 Column 0: Nonnegative integers.
%C A332529 Row 0: Upper Wythoff sequence, A001950, with 0 prepended.
%C A332529 Main Diagonal: A003231, with 0 prepended.
%C A332529 Diagonal (2,6,9,13,...) = A054770.
%C A332529 Diagonal (1,4,8,11,...) = A214971.
%C A332529 Diagonal (2,5,9,12,...) = A284624.
%F A332529 T(n,k) = floor(n + k*r), where r = (golden ratio)^2 = (3+sqrt(5))/2.
%e A332529 Northwest corner:
%e A332529   0   2    5    7   10   13   15
%e A332529   1   3    6    8   11   14   16
%e A332529   2   4    7    9   12   15   17
%e A332529   3   5    8   10   13   16   18
%e A332529   4   6    9   11   14   17   19
%e A332529   5   7   10   12   15   18   20
%e A332529   6   8   11   13   16   19   21
%e A332529 As a triangle (antidiagonals):
%e A332529   0
%e A332529   1   2
%e A332529   2   3   5
%e A332529   3   4   6   7
%e A332529   4   5   7   8  10
%t A332529 t[n_, k_] := Floor[n + k*GoldenRatio];
%t A332529 Grid[Table[t[n, k], {n, 0, 10}, {k, 0, 10}]] (* A332529 array *)
%t A332529 Table[t[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten  (* A332529 sequence *)
%Y A332529 Cf. A001950, A054770, A214971, A284624.
%K A332529 nonn,tabl,easy
%O A332529 0,2
%A A332529 _Clark Kimberling_, Jun 15 2020
%E A332529 Definition corrected by _Harvey P. Dale_, Jun 14 2022