A114538 -id:A114538 - cp's OEIS frontend

A114579 Transposition sequence of the Wythoff array.

1, 4, 6, 2, 9, 3, 7, 12, 5, 11, 10, 8, 14, 13, 18, 16, 21, 15, 34, 29, 17, 55, 47, 26, 89, 24, 144, 76, 20, 233, 123, 42, 377, 19, 610, 199, 68, 987, 39, 1597, 322, 32, 2584, 521, 110, 4181, 23, 6765, 843, 178, 10946, 63, 17711, 1364, 22, 28657, 2207, 288, 46368, 102, 75025, 3571, 52, 121393, 5778, 466, 196418, 37, 317811, 9349, 754, 514229, 165, 832040, 15127, 28, 1346269, 24476, 1220, 2178309, 267, 3524578, 39603, 84, 5702887, 64079, 1974, 9227465, 25, 14930352, 103682, 3194, 24157817, 432, 39088169, 167761, 136, 63245986, 271443, 5168

Offset: 1

Clark Kimberling, Dec 09 2005

nonn

A self-inverse permutation of the positive integers. Let s(n)=n-1+Floor(n*tau) and F(n)=n-th Fibonacci number. Then F(n+1) is in position s(n) and s(n) is in position F(n+1).

			Start with the northwest corner of the Wythoff array T (A035513):
1 2 3 5 8
4 7 11 18 29
6 10 16 26 42
9 15 24 39 63
a(1)=1 because 1=T(1,1) and T(1,1)=1.
a(2)=4 because 2=T(1,2) and T(2,1)=4.
a(3)=6 because 3=T(1,3) and T(3,1)=6.
a(15)=18 because 15=T(4,2) and T(2,4)=18.

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A035513, A114538, A114578.

Suppose (as at A114538) that T is a rectangular array consisting of all the positive integers, each exactly once. The transposition sequence of T is obtained by placing T(i, j) in position T(j, i) for all i and j.

A191427 Dispersion of ([n*r+3/2]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 11, 7, 9, 8, 19, 12, 16, 14, 10, 32, 20, 27, 24, 17, 13, 53, 33, 45, 40, 29, 22, 15, 87, 54, 74, 66, 48, 37, 25, 18, 142, 88, 121, 108, 79, 61, 41, 30, 21, 231, 143, 197, 176, 129, 100, 67, 50, 35, 23, 375, 232, 320, 286, 210, 163, 109, 82, 58, 38, 26, 608, 376, 519, 464, 341, 265, 177, 134, 95, 62, 43, 28

Offset: 1

Clark Kimberling, Jun 02 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1...3...6...11..19
  2...4...7...12..20
  5...9...16..27..45
  8...14..24..40..66
  10..17..29..48..79

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12; (* r=#rows of T, r1=#rows to show *)
c = 40; c1 = 12; (* c=#cols of T, c1=#cols to show *)
x = GoldenRatio; f[n_] := Floor[n*x + 3/2]
mex[list_] :=
NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191427 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]
(* A191427 sequence *)
(* Peter J. C. Moses, Jun 01 2011 *)

A191428 Dispersion of ([n*r+r]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 11, 8, 9, 7, 19, 14, 16, 12, 10, 32, 24, 27, 21, 17, 13, 53, 40, 45, 35, 29, 22, 15, 87, 66, 74, 58, 48, 37, 25, 18, 142, 108, 121, 95, 79, 61, 42, 30, 20, 231, 176, 197, 155, 129, 100, 69, 50, 33, 23, 375, 286, 320, 252, 210, 163, 113, 82, 55, 38, 26, 608, 464, 519, 409, 341, 265, 184, 134, 90, 63, 43, 28

Offset: 1

Clark Kimberling, Jun 03 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1...3...6...11..19
  2...4...8...14..24
  5...9...16..27..45
  7...12..21..35..58
  10..17..29..48..79

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  (* r=# rows of T, r1=# rows to show *)
c = 40; c1 = 12;  (* c=# cols of T, c1=# cols to show *)
x = GoldenRatio; f[n_] := Floor[n*x + x]
(* f(n) is complement of column 1 *)
mex[list_] :=
NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191428 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]
(* A191428 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191430 Dispersion of ([n*sqrt(2)+3/2]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 13, 17, 18, 21, 22, 19, 16, 25, 26, 31, 32, 28, 24, 20, 36, 38, 45, 46, 41, 35, 29, 23, 52, 55, 65, 66, 59, 50, 42, 34, 27, 75, 79, 93, 94, 84, 72, 60, 49, 39, 30, 107, 113, 133, 134, 120, 103, 86, 70, 56, 43, 33, 152, 161, 189, 191, 171, 147, 123, 100, 80, 62, 48, 37

Offset: 1

Clark Kimberling, Jun 03 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1...2...4...7...11
  3...5...12..18..18
  6...9...14..21..31
  10..15..22..32..46
  13..19..28..41..59

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  (* r=# rows of T to compute, r1=# rows to show *)
c = 40; c1 = 12;   (* c=# cols to compute, c1=# cols to show *)
x = Sqrt[2];
f[n_] := Floor[n*x + 3/2] (* f(n) is complement of column 1 *)
mex[list_] :=
NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];  (* the array T *)
TableForm[
Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191430 array *)
Flatten[Table[
  t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191430 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191431 Dispersion of ([n*x+x]), where x=sqrt(2) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 13, 16, 18, 21, 22, 19, 17, 24, 26, 31, 32, 28, 25, 20, 35, 38, 45, 46, 41, 36, 29, 23, 50, 55, 65, 66, 59, 52, 42, 33, 27, 72, 79, 93, 94, 84, 74, 60, 48, 39, 30, 103, 113, 132, 134, 120, 106, 86, 69, 56, 43, 34, 147, 161, 188, 190, 171, 151, 123, 98, 80, 62, 49, 37

Offset: 1

Clark Kimberling, Jun 03 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1.....2....4....7...11...16
  3.....5....8...12...18...26
  6.....9...14...21...31...45
  10...15...22...32...46...66
  13...19...28...41...59...84

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12; (* r=# rows of T, r1=# rows to show *)
c = 40; c1 = 12; (* c=# cols of T, c1=# cols to show *)
x = Sqrt[2];
f[n_] := Floor[n*x + x] (* f(n) is complement of column 1 *)
mex[list_] :=
NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[
Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191431 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]
(* A191431 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191433 Dispersion of ([n*x+n+1/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 8, 5, 4, 21, 13, 10, 6, 55, 34, 26, 16, 7, 144, 89, 68, 42, 18, 9, 377, 233, 178, 110, 47, 24, 11, 987, 610, 466, 288, 123, 63, 29, 12, 2584, 1597, 1220, 754, 322, 165, 76, 31, 14, 6765, 4181, 3194, 1974, 843, 432, 199, 81, 37, 15, 17711, 10946

Offset: 1

Clark Kimberling, Jun 03 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....21...55...144
  2....5....13...34...89...233
  4....10...26...68...178..466
  6....16...42...110..288..754
  7....18...47...123..322..843

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  (* r=# rows of T, r1=# rows to show *)
c = 40; c1 = 12;  (* c=# cols of T, c1=# cols to show *)
x = 1 + GoldenRatio;
f[n_] := Floor[n*x + 1/2] (* f(n) is complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191433 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191433 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191434 Dispersion of ([n*x+n+3/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 4, 2, 11, 6, 3, 30, 17, 9, 5, 80, 46, 25, 14, 7, 210, 121, 66, 38, 19, 8, 551, 318, 174, 100, 51, 22, 10, 1444, 834, 457, 263, 135, 59, 27, 12, 3781, 2184, 1197, 690, 354, 155, 72, 32, 13, 9900, 5719, 3135, 1807, 928, 407, 189, 85, 35, 15, 25920, 14974

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1.....4....11....30...80
  2.....6....17....46...121
  3.....9....25....66...174
  5.....14...38...100...263
  7.....19...51...135...354

Cf. A114537, A035513, A035506, A191426.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12; c = 40; c1 = 12;
x = 1 + GoldenRatio; f[n_] := Floor[n*x + 3/2]
(* f(n) is complement of column 1 *)
mex[list_] :=  NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191434 array *)
Flatten[Table[
  t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]
(* A191434 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191435 Dispersion of ([n*x+n+x]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 5, 2, 15, 7, 3, 41, 20, 10, 4, 109, 54, 28, 13, 6, 287, 143, 75, 36, 18, 8, 753, 376, 198, 96, 49, 23, 9, 1973, 986, 520, 253, 130, 62, 26, 11, 5167, 2583, 1363, 664, 342, 164, 70, 31, 12, 13529, 6764, 3570, 1740, 897, 431, 185, 83, 34, 14, 35421, 17710

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....5....15...41...109
  2....7....20...54...143
  3....10...28...75...198
  4....13...36...96...253
  6....18...49...130..342

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;  x = 1 + GoldenRatio;
f[n_] := Floor[n*x + x] (* f(n),complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191435 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191435 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191437 Dispersion of ([n*x+n+x-2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 8, 5, 4, 21, 13, 11, 6, 55, 34, 29, 16, 7, 144, 89, 76, 42, 18, 9, 377, 233, 199, 110, 47, 24, 10, 987, 610, 521, 288, 123, 63, 26, 12, 2584, 1597, 1364, 754, 322, 165, 68, 32, 14, 6765, 4181, 3571, 1974, 843, 432, 178, 84, 37, 15, 17711, 10946

Offset: 1

Clark Kimberling, Jun 04 2011

Rows 1 and 2:  Fibonacci numbers.  Rows 3 and 5: Lucas numbers.  Row n satisfies the recurrence x(n)=3*x(n-1)-x(n-2).
Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....21...55
  2....5....13...34...89
  4....11...29...76...199
  6....16...42...110..288
  7....18...47...123..322

Cf. A114537, A035513, A035506, A000045, A000032, A191426.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;  x = GoldenRatio;
f[n_] := Floor[n*x+n+x-2] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191437 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191437 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191440 Dispersion of ([n*sqrt(2)+n+3/2]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 8, 6, 4, 20, 15, 11, 5, 49, 37, 28, 13, 7, 119, 90, 69, 32, 18, 9, 288, 218, 168, 78, 44, 23, 10, 696, 527, 407, 189, 107, 57, 25, 12, 1681, 1273, 984, 457, 259, 139, 61, 30, 14, 4059, 3074, 2377, 1104, 626, 337, 148, 73, 35, 16, 9800, 7422, 5740

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....20...49
  2....6....15...37...90
  4....11...28...69...168
  5....13...32...78...189
  7....18...44...107..259

Cf. A114537, A035513, A035506, A191438, A191439, A083087.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[2];
f[n_] := Floor[n*x+n+3/2] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191440 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191440 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

cp's OEIS Frontend

A114579 Transposition sequence of the Wythoff array.

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A191427 Dispersion of ([n*r+3/2]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals.

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A191428 Dispersion of ([n*r+r]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals.

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A191430 Dispersion of ([n*sqrt(2)+3/2]), where [ ]=floor, by antidiagonals.

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A191431 Dispersion of ([n*x+x]), where x=sqrt(2) and [ ]=floor, by antidiagonals.

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A191433 Dispersion of ([n*x+n+1/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191434 Dispersion of ([n*x+n+3/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191435 Dispersion of ([n*x+n+x]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191437 Dispersion of ([n*x+n+x-2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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