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A194077
Natural interspersion of A060432; a rectangular array, by antidiagonals.
3
1, 3, 2, 5, 4, 7, 8, 6, 10, 17, 11, 9, 13, 21, 34, 14, 12, 16, 25, 39, 60, 18, 15, 20, 29, 44, 66, 97, 22, 19, 24, 33, 49, 72, 104, 147, 26, 23, 28, 38, 54, 78, 111, 155, 212, 30, 27, 32, 43, 59, 84, 118, 163, 221, 294, 35, 31, 37, 48, 65, 90, 125, 171, 230, 304
OFFSET
1,2
COMMENTS
See A194029 for definitions of natural fractal sequence and natural interspersion. Every positive integer occurs exactly once (and every pair of rows intersperse), so that as a sequence, A194077 is a permutation of the positive integers; its inverse is A194078.
EXAMPLE
Northwest corner:
1...3...5...8...11...14
2...4...6...9...12...15
7...10..13..16..20...24
17..21..25..29..33..38
34..39..44..49..54..59
MATHEMATICA
z = 70;
c[k_] := Sum[Floor[1/2 + Sqrt[2 j]], {j, 0, k}];
c = Table[c[k], {k, 1, z}] (* A060432 *)
f[n_] := If[MemberQ[c, n], 1, 1 + f[n - 1]]
f = Table[f[n], {n, 1, 600}] (* [A121997] *)
r[n_] := Flatten[Position[f, n]]
t[n_, k_] := r[n][[k]]
TableForm[Table[t[n, k], {n, 1, 7}, {k, 1, 7}]]
p = Flatten[Table[t[k, n - k + 1], {n, 1, 12}, {k, 1, n}]] (* A194077 *)
q[n_] := Position[p, n]; Flatten[Table[q[n], {n, 1, 90}]] (* A194078 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 14 2011
STATUS
approved