A151703 -id:A151703 - cp's OEIS frontend

A151704 a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.

1, 0, 2, 2, 2, 2, 6, 6, 2, 2, 6, 6, 6, 10, 18, 14, 2, 2, 6, 6, 6, 10, 18, 14, 6, 10, 18, 18, 22, 38, 50, 30, 2, 2, 6, 6, 6, 10, 18, 14, 6, 10, 18, 18, 22, 38, 50, 30, 6, 10, 18, 18, 22, 38, 50, 34, 22, 38, 54, 58, 82, 126, 130, 62, 2, 2, 6, 6, 6, 10, 18, 14, 6, 10, 18, 18, 22, 38, 50, 30, 6

Offset: 0

N. J. A. Sloane, Jun 06 2009

nonn

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Maple
```
See A151702 for Maple code.
```

a = {1, 0}; Do[AppendTo[a, 2 a[[j]] + a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)

A151705 a(0)=0, a(1)=1; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

Original entry on oeis.org

0, 1, 2, 6, 2, 6, 16, 16, 2, 6, 16, 16, 16, 44, 64, 36, 2, 6, 16, 16, 16, 44, 64, 36, 16, 44, 64, 64, 120, 216, 200, 76, 2, 6, 16, 16, 16, 44, 64, 36, 16, 44, 64, 64, 120, 216, 200, 76, 16, 44, 64, 64, 120, 216, 200, 104, 120, 216, 256, 368, 672, 832, 552, 156, 2, 6, 16, 16, 16

Offset: 0

N. J. A. Sloane, Jun 06 2009

nonn

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Maple
```
See A151702 for Maple code.
```

a = {0, 1}; Do[AppendTo[a, 2 a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)

A151706 a(0)=1, a(1)=0; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

Original entry on oeis.org

1, 0, 2, 4, 2, 4, 12, 12, 2, 4, 12, 12, 12, 32, 48, 28, 2, 4, 12, 12, 12, 32, 48, 28, 12, 32, 48, 48, 88, 160, 152, 60, 2, 4, 12, 12, 12, 32, 48, 28, 12, 32, 48, 48, 88, 160, 152, 60, 12, 32, 48, 48, 88, 160, 152, 80, 88, 160, 192, 272, 496, 624, 424, 124, 2, 4, 12, 12, 12, 32, 48

Offset: 0

N. J. A. Sloane, Jun 06 2009

nonn

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Maple
```
See A151702 for Maple code.
```

a = {1, 0}; Do[AppendTo[a, 2 a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)

A151707 a(0)=1, a(1)=1; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

Original entry on oeis.org

1, 1, 4, 10, 4, 10, 28, 28, 4, 10, 28, 28, 28, 76, 112, 64, 4, 10, 28, 28, 28, 76, 112, 64, 28, 76, 112, 112, 208, 376, 352, 136, 4, 10, 28, 28, 28, 76, 112, 64, 28, 76, 112, 112, 208, 376, 352, 136, 28, 76, 112, 112, 208, 376, 352, 184, 208, 376, 448, 640, 1168, 1456, 976, 280

Offset: 0

N. J. A. Sloane, Jun 06 2009

nonn

Equals A151705 + A151706.

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Maple
```
See A151702 for Maple code.
```

a = {1, 1}; Do[AppendTo[a, 2 a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)

A151708 a(0)=1, a(1)=2; a(2^i+j)=2a(j)+2a(j+1) for 0 <= j < 2^i.

Original entry on oeis.org

1, 2, 6, 16, 6, 16, 44, 44, 6, 16, 44, 44, 44, 120, 176, 100, 6, 16, 44, 44, 44, 120, 176, 100, 44, 120, 176, 176, 328, 592, 552, 212, 6, 16, 44, 44, 44, 120, 176, 100, 44, 120, 176, 176, 328, 592, 552, 212, 44, 120, 176, 176, 328, 592, 552, 288, 328, 592, 704, 1008, 1840, 2288

Offset: 0

N. J. A. Sloane, Jun 06 2009

nonn

Equals 2*A151705+A151706.

Ivan Neretin, Table of n, a(n) for n = 0..8191
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For the recurrence a(2^i+j) = C*a(j) + D*a(j+1), a(0) = A, a(1) = B for following values of (A B C D) see: (0 1 1 1) A118977, (1 0 1 1) A151702, (1 1 1 1) A151570, (1 2 1 1) A151571, (0 1 1 2) A151572, (1 0 1 2) A151703, (1 1 1 2) A151573, (1 2 1 2) A151574, (0 1 2 1) A160552, (1 0 2 1) A151704, (1 1 2 1) A151568, (1 2 2 1) A151569, (0 1 2 2) A151705, (1 0 2 2) A151706, (1 1 2 2) A151707, (1 2 2 2) A151708.

Maple
```
See A151702 for Maple code.
```

a = {1, 2}; Do[AppendTo[a, 2 a[[j]] + 2 a[[j + 1]]], {i, 6}, {j, 2^i}]; a (* Ivan Neretin, Jul 04 2017 *)

A151691 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + x^(2^k)).

Original entry on oeis.org

1, 2, 1, 2, 5, 4, 1, 2, 5, 4, 5, 12, 13, 6, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 5, 12, 13, 14, 29, 38, 25, 16, 29, 38, 41, 72, 105, 88, 41, 10, 1, 2, 5, 4, 5, 12, 13, 6, 5, 12, 13, 14, 29, 38, 25, 8, 5, 12, 13, 14, 29

Offset: 0

N. J. A. Sloane, Jun 04 2009

nonn

			From _Omar E. Pol_, Jun 09 2009: (Start)
Triangle begins:
  1;
  2,1;
  2,5,4,1;
  2,5,4,5,12,13,6,1;
  2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,1;
  2,5,4,5,12,13,6,5,12,13,14,29,38,25,8,5,12,13,14,29,38,25,16,29,38,41,72,...
(End)

David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

For generating functions of the form Product_{k>=c} (1 + a*x^(2^k-1) + b*x^2^k) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694.
Cf. A151685. See A151703 for another version with a simpler recurrence.
Cf. A000079. - Omar E. Pol, Jun 09 2009

cp's OEIS Frontend

A151704 a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A151705 a(0)=0, a(1)=1; a(2^i+j) = 2*a(j) + 2*a(j+1) for 0 <= j < 2^i.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A151706 a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + 2*a(j+1) for 0 <= j < 2^i.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A151707 a(0)=1, a(1)=1; a(2^i+j) = 2*a(j) + 2*a(j+1) for 0 <= j < 2^i.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A151708 a(0)=1, a(1)=2; a(2^i+j)=2*a(j)+2*a(j+1) for 0 <= j < 2^i.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A151691 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + x^(2^k)).

Views

Author

Keywords

Examples

Links

Crossrefs

A151705 a(0)=0, a(1)=1; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

A151706 a(0)=1, a(1)=0; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

A151707 a(0)=1, a(1)=1; a(2^i+j) = 2a(j) + 2a(j+1) for 0 <= j < 2^i.

A151708 a(0)=1, a(1)=2; a(2^i+j)=2a(j)+2a(j+1) for 0 <= j < 2^i.