A361995 Order array of A361993, read by descending antidiagonals.

1, 2, 4, 3, 6, 7, 5, 10, 11, 8, 9, 16, 18, 14, 12, 15, 26, 29, 23, 19, 13, 24, 42, 46, 38, 31, 22, 17, 39, 68, 74, 62, 50, 36, 28, 20, 63, 110, 119, 100, 81, 59, 45, 32, 21, 102, 111, 192, 101, 131, 97, 73, 52, 35, 25, 165, 179, 310, 162, 212, 158, 118, 84

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    3    5    9   15   24 ...
   4    6   10   16   26   42   68 ...
   7   11   18   29   46   74  119 ...
   8   14   23   38   62  100  162 ...
  12   19   31   50   81  131  212 ...
  13   22   36   59   97  158  191 ...
  ...
		

Crossrefs

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

Programs

Mathematica

zz = 300; z = 40;
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, k] + w[2 h, 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}]]  (*A351995, array*)
v = Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (*A351995, sequence*)