A361995 - OEIS

%I #8 Apr 07 2023 17:38:16

%S 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,

%T 22,17,39,68,74,62,50,36,28,20,63,110,119,100,81,59,45,32,21,102,111,

%U 192,101,131,97,73,52,35,25,165,179,310,162,212,158,118,84

%N Order array of A361993, read by descending antidiagonals.

%C 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.

%e Corner:

%e    1    2    3    5    9   15   24 ...

%e    4    6   10   16   26   42   68 ...

%e    7   11   18   29   46   74  119 ...

%e    8   14   23   38   62  100  162 ...

%e   12   19   31   50   81  131  212 ...

%e   13   22   36   59   97  158  191 ...

%e   ...

%t zz = 300; z = 40;

%t w[n_, k_] := w[n, k] = Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];

%t b[h_, k_] := b[h, k] = w[2 h - 1, k] + w[2 h, k];

%t s = Flatten[Table[b[h, k], {h, 1, zz}, {k, 1, z}]];

%t r[h_, k_] := Length[Select[s, # <= b[h, k] &]]

%t TableForm[Table[r[h, k], {h, 1, 50}, {k, 1, 12}]]  (*A351995, array*)

%t v = Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (*A351995, sequence*)

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

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Apr 05 2023