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A361996
Order array of A361994, read by descending antidiagonals.
3
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
1,2
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.
EXAMPLE
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 ...
...
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 05 2023
STATUS
approved