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