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A361995
Order array of A361993, read by descending antidiagonals.
1
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Apr 05 2023
STATUS
approved