A347065
Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = (1+sqrt(5))/2, h >= 1, 0 <= m <= n}.
Original entry on oeis.org
1, 3, 1, 4, 3, 1, 6, 5, 3, 1, 8, 7, 5, 3, 1, 9, 9, 7, 5, 3, 1, 11, 11, 10, 7, 5, 3, 1, 12, 13, 12, 10, 7, 5, 3, 1, 14, 15, 14, 12, 10, 7, 5, 3, 1, 16, 17, 16, 15, 12, 10, 7, 5, 3, 1, 17, 19, 19, 17, 15, 12, 10, 7, 5, 3, 1, 19, 21, 21, 20, 17, 15, 12, 10, 7
Offset: 1
Corner:
1 3 4 6 8 9 11 12 14 16 17 19 21
1 3 5 7 9 11 13 15 17 19 21 23 25
1 3 5 7 10 12 14 16 19 21 23 25 28
1 3 5 7 10 12 15 17 20 22 24 26 29
1 3 5 7 10 12 15 17 20 22 24 27 30
1 3 5 7 10 12 15 17 20 22 24 27 30
1 3 5 7 10 12 15 17 20 22 24 27 30
-
z = 100; r = N[(1 + Sqrt[5])/2];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347065, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347065, sequence *)
A347066
Rectangular array (T(n,k)), by antidiagonals: T(n,k) is the position of k in the ordering of {h/r^m, r = sqrt(2), h >= 1, 0 <= m <= n}.
Original entry on oeis.org
1, 3, 1, 5, 3, 1, 6, 6, 3, 1, 8, 7, 7, 3, 1, 10, 10, 8, 7, 3, 1, 11, 12, 11, 8, 7, 3, 1, 13, 14, 14, 12, 8, 7, 3, 1, 15, 16, 16, 15, 12, 8, 7, 3, 1, 17, 19, 18, 17, 16, 12, 8, 7, 3, 1, 18, 21, 21, 19, 18, 16, 12, 8, 7, 3, 1, 20, 23, 23, 23, 20, 18, 16, 12, 8
Offset: 1
Corner:
1, 3, 5, 6, 8, 10, 11, 13, 15, 17, 18, 20, ...
1, 3, 6, 7, 10, 12, 14, 16, 19, 21, 23, 25, ...
1, 3, 7, 8, 11, 14, 16, 18, 21, 23, 25, 28, ...
1, 3, 7, 8, 12, 15, 17, 19, 23, 25, 27, 30, ...
1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
1, 3, 7, 8, 12, 16, 18, 20, 24, 26, 28, 32, ...
...
-
z = 100; r = N[Sqrt[2]];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347066, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347066, sequence *)
A347067
Rectangular array (T(n,k)), by antidiagonals: T(n,k) = position of k in the ordering of {h/r^m, r = 1/sqrt(2), h >= 1, 0 <= m <= n}.
Original entry on oeis.org
2, 4, 4, 7, 8, 6, 9, 13, 13, 10, 12, 17, 21, 21, 15, 14, 21, 28, 33, 32, 19, 16, 22, 34, 44, 49, 40, 25, 19, 26, 35, 54, 66, 61, 51, 41, 21, 30, 41, 55, 82, 82, 78, 83, 63, 24, 35, 48, 65, 83, 102, 105, 126, 128, 95, 26, 38, 56, 76, 98, 103, 130, 169, 193
Offset: 1
Corner:
2, 4, 7, 9, 12, 14, 16, 19, 21, ...
4, 8, 13, 17, 21, 22, 26, 30, 35, ...
6, 13, 21, 28, 34, 35, 41, 48, 56, ...
10, 21, 33, 44, 54, 55, 65, 76, 88, ...
15, 32, 49, 66, 82, 83, 98, 115, 133, ...
19, 40, 61, 82, 102, 103, 122, 143, 165, ...
25, 51, 78, 105, 130, 131, 156, 183, 210, ...
41, 83, 126, 169, 210, 211, 252, 283, 310, ...
...
-
z = 100; r = N[1/Sqrt[2]];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347067, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347067, sequence *)
A347068
Rectangular array (T(n,k)), by downward antidiagonals: T(n,k) = position of k in the ordering of {h*r^m, r = 1/(golden ratio), h >= 1, 0 <= m <= n}.
Original entry on oeis.org
2, 5, 4, 7, 10, 8, 10, 14, 18, 14, 13, 20, 26, 31, 25, 15, 26, 36, 46, 53, 42, 18, 30, 47, 63, 79, 88, 71, 20, 36, 55, 81, 107, 132, 146, 117, 23, 40, 65, 96, 136, 178, 219, 239, 193, 26, 46, 73, 112, 162, 225, 294, 359, 391, 315, 28, 52, 84, 127, 189, 269
Offset: 1
Corner:
2, 5, 7, 10, 13, 15, 18, 20, 23, ...
4, 10, 14, 20, 26, 30, 36, 40, 46, ...
8, 18, 26, 36, 47, 55, 65, 73, 84, ...
14, 31, 46, 63, 81, 96, 112, 127, 145, ...
25, 53, 79, 107, 136, 162, 189, 215, 244, ...
42, 88, 132, 178, 225, 269, 314, 358, 405, ...
71, 146, 219, 294, 370, 443, 517, 590, 666, ...
...
-
z = 1000; r = N[(-1+Sqrt[5])/2];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347068, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347068, sequence *)
Showing 1-4 of 4 results.
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