This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332502 #10 Jan 08 2021 22:17:13 %S A332502 0,1,1,3,2,2,4,4,3,3,6,5,5,4,4,8,7,6,6,5,5,9,9,8,7,7,6,6,11,10,10,9,8, %T A332502 8,7,7,12,12,11,11,10,9,9,8,8,14,13,13,12,12,11,10,10,9,9,16,15,14,14, %U A332502 13,13,12,11,11,10,10,17,17,16,15,15,14,14,13 %N A332502 Rectangular array read by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2. %C A332502 Every nonnegative integer occurs exactly once in the union of row 0 and the main diagonal. %C A332502 Column 0: Nonnegative integers, A001477. %C A332502 Row 0: Lower Wythoff sequence, A000201. %C A332502 Row 1: A026351. %C A332502 Row 2: A026355 (and essentially A099267). %C A332502 Main Diagonal: Upper Wythoff sequence, A001950. %C A332502 Diagonal (1,4,6,9,...) = A003622; %C A332502 Diagonal (3,5,8,11,...) = A026274; %C A332502 Diagonal (1,3,6,8,...) = A026352; %C A332502 Diagonal (2,4,7,9,...) = A026356. %F A332502 T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2. %e A332502 Northwest corner: %e A332502 0 1 3 4 6 8 9 11 12 14 16 %e A332502 1 2 4 5 7 9 10 12 13 15 17 %e A332502 2 3 5 6 8 10 11 13 14 16 18 %e A332502 3 4 6 7 9 11 12 14 15 17 19 %e A332502 4 5 7 8 10 12 13 15 16 18 20 %e A332502 5 6 8 9 11 13 14 16 17 19 21 %e A332502 As a triangle (antidiagonals): %e A332502 0 %e A332502 1 1 %e A332502 2 2 3 %e A332502 3 3 4 4 %e A332502 4 4 5 5 6 %e A332502 5 5 6 6 7 8 %e A332502 6 6 7 7 8 9 9 %t A332502 t[n_, k_] := Floor[n + k*GoldenRatio]; %t A332502 Grid[Table[t[n, k], {n, 0, 10}, {k, 0, 10}]] (* array *) %t A332502 u = Table[t[n - k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* sequence *) %Y A332502 Cf. A000210, A001950, A001622, A084531, A167267, A019446. %K A332502 nonn,tabl,easy %O A332502 0,4 %A A332502 _Clark Kimberling_, May 08 2020