A160736 -id:A160736 - cp's OEIS frontend

A160740 Toothpick sequence starting from a cross formed by 4 toothpicks.

0, 4, 8, 16, 24, 32, 40, 56, 72, 80, 88, 104, 120, 136, 160, 200, 232, 240, 248, 264, 280, 296, 320, 360, 392, 408, 432, 472, 512, 560, 640, 744, 808, 816, 824, 840, 856, 872, 896, 936, 968, 984, 1008, 1048, 1088, 1136, 1216, 1320, 1384, 1400, 1424, 1464, 1504, 1552

Offset: 0

Omar E. Pol, May 25 2009

nonn

On the infinite square grid we start at stage 0 with no toothpicks. Toothpicks have length 2. At stage 1 we place two consecutive toothpicks in the vertical direction and two consecutive toothpicks in the horizontal direction forming a cross centered at the origin. At stage 2 we place four toothpicks. At stage 3 we place eight toothpicks. For more information about the toothpick sequences see A139250. - Omar E. Pol, Nov 24 2011

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.], which is also available at arXiv:1004.3036v2
Mathematical Association of America, NumberADay: 1136
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
Index entries for sequences related to toothpick sequences

Cf. A139250, A139251, A160736, A160738, A160741.

Cf. A160170, A160426, A194432, A194434.

a(n) = 4*A160406(n).

More terms from N. J. A. Sloane, May 25 2009

A160738 Toothpick sequence starting from a T formed by 3 toothpicks: a(n)=A160406(n)*3.

Original entry on oeis.org

0, 3, 6, 12, 18, 24, 30, 42, 54, 60, 66, 78, 90, 102, 120, 150, 174, 180, 186, 198, 210, 222, 240, 270, 294, 306, 324, 354, 384, 420, 480, 558, 606, 612, 618, 630, 642, 654, 672, 702, 726, 738, 756, 786, 816, 852, 912, 990, 1038, 1050, 1068, 1098, 1128, 1164

Offset: 0

Omar E. Pol, May 25 2009, Jun 19 2009

nonn

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

Cf. A139250, A139251, A160736, A160737, A160739, A160740.

More terms from R. J. Mathar, Jul 28 2009

A160730 Toothpick sequence starting from a right angle formed by two toothpicks.

Original entry on oeis.org

0, 2, 4, 8, 14, 20, 26, 38, 52, 64, 70, 82, 96, 112, 130, 162, 196, 216, 222, 234, 248, 264, 282, 314, 348, 372, 390, 422, 460, 504, 566, 658, 740, 776, 782, 794, 808, 824, 842, 874, 908, 932, 950, 982, 1020, 1064

Offset: 0

Omar E. Pol, May 25 2009

nonn

Nathaniel Johnston, Table of n, a(n) for n = 0..255
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
Nathaniel Johnston, C script

Cf. A139250, A160736, A160731.

Terms after a(11) from Nathaniel Johnston, Mar 28 2011

A160158 Toothpick sequence starting from a segment of length 4 formed by two toothpicks.

Original entry on oeis.org

0, 2, 4, 8, 16, 24, 28, 36, 48, 56, 64, 80, 104, 124, 136, 156, 176, 184, 192, 208, 232, 252, 268, 296, 328, 352, 384, 440, 508, 560, 600, 652, 688, 696, 704, 720, 744, 764, 780, 808, 840, 864, 896, 952, 1020, 1072, 1116, 1176, 1224, 1248, 1280, 1336, 1404

Offset: 0

Omar E. Pol, May 29 2009

nonn

The sequence gives the number of toothpicks in the sieve after n-th stage.

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

Cf. A139250, A160406, A160730, A160732, A160736, A160738, A160740.

Extended beyond a(13) by R. J. Mathar, Jun 01 2009

A160162 a(n) = A160158(n)/2.

Original entry on oeis.org

0, 1, 2, 4, 8, 12, 14, 18, 24, 28, 32, 40, 52, 62, 68, 78, 88, 92, 96, 104, 116, 126, 134, 148, 164, 176, 192, 220, 254, 280, 300, 326, 344, 348, 352, 360, 372, 382, 390, 404, 420, 432, 448, 476, 510, 536, 558, 588, 612, 624, 640, 668, 702, 730, 760, 804, 848

Offset: 0

Omar E. Pol, May 29 2009

nonn

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

Cf. A139250, A160158, A160406, A160730, A160732, A160736, A160738, A160740.

Extended beyond a(13) by R. J. Mathar, Jun 01 2009

A160732 Toothpick sequence starting from a T formed by three toothpicks.

Original entry on oeis.org

0, 3, 6, 12, 20, 28, 34, 46, 60, 68, 76, 92, 112, 130, 148, 178, 204, 212, 220, 236, 256, 274, 294, 328, 360, 380, 408, 456, 510, 560, 620, 698, 748, 756, 764, 780, 800, 818, 838, 872, 904, 924, 952, 1000

Offset: 0

Omar E. Pol, May 25 2009

nonn

Nathaniel Johnston, Table of n, a(n) for n = 0..274
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
Nathaniel Johnston, C script for computing table of terms

Cf. A139250, A160732, A160733, A160736, A160738, A160740.

Terms after a(9) from Nathaniel Johnston, Mar 30 2011

A160744 a(n) = A151566(n)*3.

Original entry on oeis.org

0, 3, 6, 12, 18, 24, 30, 42, 54, 60, 66, 78, 90, 102, 114, 138, 162, 168, 174, 186, 198, 210, 222, 246, 270, 282, 294, 318, 342, 366, 390, 438, 486, 492, 498, 510, 522, 534, 546, 570, 594, 606, 618, 642, 666, 690, 714, 762, 810, 822, 834, 858, 882, 906, 930

Offset: 0

Omar E. Pol, May 25 2009

nonn

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

Cf. A139250, A151566, A160720, A160722, A160736, A160738, A160740, A160742, A160746.

More terms from R. J. Mathar, Jul 28 2009

A160742 a(n) = A151566(n)*2.

Original entry on oeis.org

0, 2, 4, 8, 12, 16, 20, 28, 36, 40, 44, 52, 60, 68, 76, 92, 108, 112, 116, 124, 132, 140, 148, 164, 180, 188, 196, 212, 228, 244, 260, 292, 324, 328, 332, 340, 348, 356, 364, 380, 396, 404, 412, 428, 444, 460, 476, 508, 540, 548, 556, 572, 588, 604, 620, 652, 684

Offset: 0

Omar E. Pol, May 25 2009

nonn

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

Cf. A139250, A151566, A160720, A160722, A160736, A160738, A160740, A160744, A160746.

More terms from Jinyuan Wang, Mar 14 2020

A160746 a(n) = A151566(n)*4.

Original entry on oeis.org

0, 4, 8, 16, 24, 32, 40, 56, 72, 80, 88, 104, 120, 136, 152, 184, 216, 224, 232, 248, 264, 280, 296, 328, 360, 376, 392, 424, 456, 488, 520, 584, 648, 656, 664, 680, 696, 712, 728, 760, 792, 808, 824, 856, 888, 920, 952, 1016, 1080, 1096, 1112, 1144, 1176, 1208, 1240

Offset: 0

Omar E. Pol, May 25 2009

nonn

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

Cf. A139250, A151566, A160720, A160722, A160736, A160738, A160740, A160742, A160744.

More terms from N. J. A. Sloane, May 25 2009

cp's OEIS Frontend

A160740 Toothpick sequence starting from a cross formed by 4 toothpicks.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions

A160738 Toothpick sequence starting from a T formed by 3 toothpicks: a(n)=A160406(n)*3.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160730 Toothpick sequence starting from a right angle formed by two toothpicks.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160158 Toothpick sequence starting from a segment of length 4 formed by two toothpicks.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions

A160162 a(n) = A160158(n)/2.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160732 Toothpick sequence starting from a T formed by three toothpicks.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160744 a(n) = A151566(n)*3.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160742 a(n) = A151566(n)*2.

Views

Author

Keywords

Links

Crossrefs

Extensions

A160746 a(n) = A151566(n)*4.

Views

Author

Keywords

Links

Crossrefs

Extensions