A050032 -id:A050032 - cp's OEIS frontend

A050052 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 4.

1, 2, 4, 5, 9, 10, 14, 23, 37, 38, 42, 51, 65, 102, 144, 209, 353, 354, 358, 367, 381, 418, 460, 525, 669, 1022, 1380, 1761, 2221, 2890, 4270, 6491, 10761, 10762, 10766, 10775, 10789, 10826, 10868, 10933, 11077, 11430, 11788

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Same as A050036 and A050068 except for second term.

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 2, 4][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 4}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050036 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.

Original entry on oeis.org

1, 1, 4, 5, 9, 10, 14, 23, 37, 38, 42, 51, 65, 102, 144, 209, 353, 354, 358, 367, 381, 418, 460, 525, 669, 1022, 1380, 1761, 2221, 2890, 4270, 6491, 10761, 10762, 10766, 10775, 10789, 10826, 10868, 10933, 11077, 11430, 11788

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Same as A050052 and A050068 except for second term.

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 1, 4][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 1, 4}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050040 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 1.

Original entry on oeis.org

1, 2, 1, 2, 3, 4, 5, 8, 13, 14, 15, 18, 23, 36, 51, 74, 125, 126, 127, 130, 135, 148, 163, 186, 237, 362, 489, 624, 787, 1024, 1513, 2300, 3813, 3814, 3815, 3818, 3823, 3836, 3851, 3874, 3925, 4050, 4177, 4312, 4475, 4712, 5201

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 2, 1][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 1}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050044 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 2.

Original entry on oeis.org

1, 2, 2, 3, 5, 6, 8, 13, 21, 22, 24, 29, 37, 58, 82, 119, 201, 202, 204, 209, 217, 238, 262, 299, 381, 582, 786, 1003, 1265, 1646, 2432, 3697, 6129, 6130, 6132, 6137, 6145, 6166, 6190, 6227, 6309, 6510, 6714, 6931, 7193, 7574, 8360

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 2, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 2}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050048 a(n) = a(n-1) + a(m) for n >= 3, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = 2.

Original entry on oeis.org

1, 2, 3, 4, 7, 8, 11, 18, 29, 30, 33, 40, 51, 80, 113, 164, 277, 278, 281, 288, 299, 328, 361, 412, 525, 802, 1083, 1382, 1743, 2268, 3351, 5094, 8445, 8446, 8449, 8456, 8467, 8496, 8529, 8580, 8693, 8970, 9251, 9550, 9911, 10436

Offset: 1

Clark Kimberling

nonn

In the Mathematica program below, the author of the program uses the initial conditions a(1) = 1, a(2) = 2, and a(3) = 3. This is not necessary. We get the same sequence using the initial conditions a(1) = 1 and a(2) = 2. - Petros Hadjicostas, Nov 14 2019

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 3, [1, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 2, 3}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050056 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 1.

Original entry on oeis.org

1, 3, 1, 2, 3, 4, 5, 8, 13, 14, 15, 18, 23, 36, 51, 74, 125, 126, 127, 130, 135, 148, 163, 186, 237, 362, 489, 624, 787, 1024, 1513, 2300, 3813, 3814, 3815, 3818, 3823, 3836, 3851, 3874, 3925, 4050, 4177, 4312, 4475, 4712, 5201

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050060 (1,3,2), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember; `if`(n < 4, [1, 3, 1][n],
       a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 15 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 1}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 15 2019

A050060 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 2.

Original entry on oeis.org

1, 3, 2, 3, 5, 6, 8, 13, 21, 22, 24, 29, 37, 58, 82, 119, 201, 202, 204, 209, 217, 238, 262, 299, 381, 582, 786, 1003, 1265, 1646, 2432, 3697, 6129, 6130, 6132, 6137, 6145, 6166, 6190, 6227, 6309, 6510, 6714, 6931, 7193, 7574, 8360

Offset: 1

Clark Kimberling

nonn

Variant of A050028 and A050044. - R. J. Mathar, Oct 15 2008

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050064 (1,3,3), A050068 (1,3,4).

a := proc(n) option remember;
`if`(n < 4, [1, 3, 2][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
end proc:
seq(a(n), n = 1..60); # Petros Hadjicostas, Nov 14 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 2}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 14 2019

A050064 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

Original entry on oeis.org

1, 3, 3, 4, 7, 8, 11, 18, 29, 30, 33, 40, 51, 80, 113, 164, 277, 278, 281, 288, 299, 328, 361, 412, 525, 802, 1083, 1382, 1743, 2268, 3351, 5094, 8445, 8446, 8449, 8456, 8467, 8496, 8529, 8580, 8693, 8970, 9251, 9550, 9911, 10436

Offset: 1

Clark Kimberling

nonn

Variant of A050032 or A050048. - R. J. Mathar, Oct 15 2008

Ivan Neretin, Table of n, a(n) for n = 1..8193

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050068 (1,3,4).

a := proc(n) option remember;
     `if`(n < 4, [1, 3, 3][n], a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3)):
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 18 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 3}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 18 2019

A050068 a(n) = a(n-1) + a(m) for n >= 3, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = 3.

Original entry on oeis.org

1, 3, 4, 5, 9, 10, 14, 23, 37, 38, 42, 51, 65, 102, 144, 209, 353, 354, 358, 367, 381, 418, 460, 525, 669, 1022, 1380, 1761, 2221, 2890, 4270, 6491, 10761, 10762, 10766, 10775, 10789, 10826, 10868, 10933, 11077, 11430, 11788

Offset: 1

Clark Kimberling

nonn

The author of the Mathematica program below uses the initial conditions a(1) = 1, a(2) = 3, and a(3) = 4. This is not necessary. We get the same sequence by using the initial conditions a(1) = 1 and a(2) = 3. - Petros Hadjicostas, Nov 15 2019

Ivan Neretin, Table of n, a(n) for n = 1..8193

Same as A050036 and A050052 except for the second term.

Cf. similar sequences with different initial conditions: A050024 (1,1,1), A050028 (1,1,2), A050032 (1,1,3), A050036 (1,1,4), A050040 (1,2,1), A050044 (1,2,2), A050048 (1,2,3), A050052 (1,2,4), A050056 (1,3,1), A050060 (1,3,2), A050064 (1,3,3).

a := proc(n) option remember; `if`(n < 3, [1,3][n],
        a(n - 1) + a(-2^ceil(log[2](n - 1)) + 2*n - 3))
     end proc:
seq(a(n), n = 1..40); # Petros Hadjicostas, Nov 15 2019

Fold[Append[#1, #1[[-1]] + #1[[#2]]] &, {1, 3, 4}, Flatten@Table[2 k - 1, {n, 5}, {k, 2^n}]] (* Ivan Neretin, Sep 07 2015 *)

Name edited by Petros Hadjicostas, Nov 15 2019

cp's OEIS Frontend

A050052 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 4.

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A050036 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and 2^p < n - 1 <= 2^(p+1), starting with a(1) = a(2) = 1 and a(3) = 4.

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Maple

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A050040 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 2, and a(3) = 1.

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Programs

Maple

Mathematica

Extensions

A050044 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 2.

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Maple

Mathematica

Extensions

A050048 a(n) = a(n-1) + a(m) for n >= 3, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = 2.

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Programs

Maple

Mathematica

Extensions

A050056 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 1.

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Programs

Maple

Mathematica

Extensions

A050060 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1, a(2) = 3, and a(3) = 2.

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Crossrefs

Programs

Maple

Mathematica

Extensions

A050064 a(n) = a(n-1) + a(m) for n >= 4, where m = 2*n - 3 - 2^(p+1) and p is the unique integer such that 2^p < n - 1 <= 2^(p+1), starting with a(1) = 1 and a(2) = a(3) = 3.

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