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

1,2

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.

Links

Table of n, a(n) for n=1..63.

Example

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 ...
  ...

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*)

Crossrefs

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

Sequence in context: A194030 A353658 A083044 * A126714 A035506 A246368

Adjacent sequences: A361992 A361993 A361994 * A361996 A361997 A361998

Keyword

nonn,tabl

Author

Clark Kimberling, Apr 05 2023

Status

approved