A361996 Order array of A361994, read by descending antidiagonals.

1, 2, 3, 6, 7, 4, 15, 17, 11, 5, 39, 43, 28, 14, 8, 102, 112, 73, 38, 20, 9, 268, 292, 191, 100, 51, 23, 10, 568, 592, 491, 263, 132, 61, 27, 12, 868, 892, 791, 563, 345, 159, 72, 32, 13, 1168, 1192, 1091, 863, 645, 416, 189, 83, 35, 16, 1468, 1492, 1391

Offset: 1

Author

Clark Kimberling, Apr 05 2023

Keywords

• nonn
• tabl

Comments

This array is an interspersion (hence a dispersion, as in A114537 and A163255), so every positive integer occurs exactly once. See A333029 for the definition of order array.

Examples

			Corner:
  1    2    6   15   39  102  268 ...
  3    7   17   43  112  292  592 ...
  4   11   28   73  191  491  791 ...
  5   14   38  100  263  563  863 ...
  8   20   51  132  345  645  945 ...
  9   23   61  159  416  716 1016 ...
  ...
		

Crossrefs

Cf. A114537, A163255, A333029, A361993, A361996.

Programs

Mathematica

zz = 300; z = 30;
w[n_, k_] := w[n, k] = Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
b[h_, k_] := b[h, k] = w[2 h - 1, 2 k - 1] + w[2 h - 1, 2 k] + w[2 h, 2 k - 1] + w[2 h, 2 k];
s = Flatten[Table[b[h, k], {h, 1, zz}, {k, 1, z}]];
r[h_, k_] := Length[Select[s, # <= b[h, k] &]]
TableForm[Table[r[h, k], {h, 1, 50}, {k, 1, 12}]](*A351996, array*)
v = Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (*A351996, sequence *)