cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A161831 First differences of A161830.

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 4, 8, 4, 4, 4, 8, 6, 8, 10, 18, 10, 4
Offset: 1

Views

Author

Omar E. Pol, Jun 20 2009

Keywords

Comments

Number of Y-toothpicks added to the sieve at the n-th round.

Links

Crossrefs

Cf. A139250, A139251, A160121, A160407, A161830, A161832, A161833.

A161832 a(n) = (A161830(n+1)-1)/2.

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 9, 13, 15, 17, 19, 23, 26, 30, 35, 44, 49, 51
Offset: 0

Views

Author

Omar E. Pol, Jun 20 2009

Keywords

Comments

The sequence gives the number of Y-toothpicks in the structure after n rounds. A161833 (the first differences) gives the number added at the n-th round.
See the Y-toothpick sequence A160120 and A161830 for more information.

Links

Crossrefs

Cf. A139250, A160120, A160406, A161830, A161831, A161833.

A160407 First differences of toothpick numbers A160406.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 4, 4, 2, 2, 4, 4, 4, 6, 10, 8, 2, 2, 4, 4, 4, 6, 10, 8, 4, 6, 10, 10, 12, 20, 26, 16, 2, 2, 4, 4, 4, 6, 10, 8, 4, 6, 10, 10, 12, 20, 26, 16, 4, 6, 10, 10, 12, 20, 26, 18, 12, 20, 28, 30, 42
Offset: 1

Views

Author

Omar E. Pol, May 23 2009

Keywords

Comments

Number of toothpicks added at n-th stage in the toothpick structure of A160406.
From Omar E. Pol, Mar 15 2020: (Start)
The cellular automaton described in A160406 has word "ab", so the structure of this triangle is as follows:
a,b;
a,b;
a,b,a,b;
a,b,a,b,a,b,a,b;
a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b;
...
The row lengths are the terms of A011782 multiplied by 2, equaling the column 2 of the square array A296612: 2, 2, 4, 8, 16, ...
This arrangement has the property that the odd-indexed columns (a) contain numbers of the toothpicks that are parallel to initial toothpick, and the even-indexed columns (b) contain numbers of the toothpicks that are orthogonal to the initial toothpick.
For further information about the "word" of a cellular automaton see A296612. (End)

Examples

			From _Omar E. Pol_, Jul 18 2009, Mar 15 2020: (Start)
If written as a triangle:
1,1;
2,2;
2,2,4,4;
2,2,4,4,4,6,10,8;
2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16;
2,2,4,4,4,6,10,8,4,6,10,10,12,20,26,16,4,6,10,10,12,20,26,18,12,20,28,30,42;...
(End)

Links

Crossrefs

Cf. A011782, A139250, A139251, A153000, A153006, A152980, A160406, A161830, A161831, A296612.

Extensions

More terms from N. J. A. Sloane, Jul 17 2009

A194440 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "wide" triangle of the second kind.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 19, 27, 35, 39, 43, 51, 63, 79, 87, 103, 119, 123, 127, 135, 147, 163, 179, 203, 229, 253, 265, 285, 313, 353, 373, 405, 437, 441, 445, 453, 465, 481, 497, 521, 547, 571, 591, 623, 663, 727, 767, 815, 869, 909, 921, 941, 973, 1021
Offset: 0

Views

Author

Omar E. Pol, Aug 29 2011

Keywords

Comments

For the D-toothpick "narrow" triangle of the second kind see A194442.
The structure is essentially one of the wedges of several D-toothpick structures. For more information see A194270. The first differences (A194441) give the number of toothpicks or D-toothpicks added at n-th stage. [Omar E. Pol, Dec 29 2012]

Links

Crossrefs

Cf. A139250, A160120, A160406, A161830, A194270, A194277, A194441, A194442, A194444, A194692, A194693, A194696, A220494, A220520.

A194442 Number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "narrow" triangle of the second kind.

Original entry on oeis.org

0, 1, 3, 7, 11, 15, 19, 26, 34, 38, 42, 50, 62, 70, 78, 91, 107, 111, 115, 123, 135, 151, 167, 187, 211, 223, 231, 247, 275, 291, 307, 332, 364, 368, 372, 380, 392, 408, 424, 446, 478, 504, 524, 548, 588, 620, 660, 693, 741, 761, 769, 785, 813, 853, 897, 947
Offset: 0

Views

Author

Omar E. Pol, Aug 29 2011

Keywords

Comments

If n = 2^k, k >= 1, then the structure looks like an isosceles triangle. For the D-toothpick "wide" triangle of the second kind see A194440.
The structure is essentially one of the wedges of several D-toothpick structures. For more information see A194270. The first differences (A194443) give the number of toothpicks or D-toothpicks added at n-th stage. - Omar E. Pol, Mar 28 2013

Links

Crossrefs

Cf. A047999, A139250, A160120, A160406, A161830, A194270, A194277, A194440, A194443, A194444, A194694, A194695, A194697, A220496, A220522.

A233970 Toothpick sequence on hexagonal net starting from the vertex of a 60-degree wedge (see Comments lines for precise definition).

Original entry on oeis.org

0, 1, 3, 5, 9, 11, 15, 21, 29, 31, 35, 41, 51, 61, 69, 83, 99, 101, 105, 111, 121, 131, 141, 159, 183, 205, 213, 227, 249, 275, 291, 321, 353, 355, 359, 365, 375, 385, 395, 413, 437, 459, 469, 487, 515, 553, 581, 627, 683, 737, 745, 759, 781, 807
Offset: 0

Views

Author

Omar E. Pol, Dec 18 2013

Keywords

Comments

Toothpicks are connected by their endpoints. The toothpicks placed in north direction are prohibited. The sequence gives the number of toothpicks after n-th stage in the structure. A233971 (the first differences) give the number of toothpicks added at n-th stage.
First differs from A169780 at a(24).
First differs from both A233764 and A233780 at a(25).

Links

Crossrefs

Cf. A139250, A161206, A161830, A169780, A182632, A182634, A182634, A182840, A233760, A233764, A233780, A233971, A233972.

A161833 First differences of A161832.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 4, 2, 2, 2, 4, 3, 4, 5, 9, 5, 2
Offset: 1

Views

Author

Omar E. Pol, Jun 20 2009

Keywords

Comments

Number of Y-toothpicks added to the sieve at the n-th round.

Links

Crossrefs

Cf. A139251, A160121, A160407, A161830, A161831, A161832.

Formula

a(n) = A161831(n+1)/2.

A161426 Y-toothpick sequence starting at the outside corner of an infinite triangle-shaped polygon as the sieve of A160120 after 2^k rounds.

Original entry on oeis.org

0, 1, 4, 7, 14, 19, 26, 35, 52, 63, 70
Offset: 0

Views

Author

Omar E. Pol and David Applegate, Jun 20 2009

Keywords

Comments

The sequence gives the number of Y-toothpicks after n rounds. A161427 (the first differences) gives the number added at the n-th round.
See the entries A160120, A139250 and A153006 for more information.

Links

Crossrefs

Cf. A000079, A139250, A153006, A160120, A161427, A161830.

A161910 Y-toothpick sequence starting at the corner of an infinite hexagon from which protrudes a half toothpick with an angle = Pi/6.

Original entry on oeis.org

0, 1, 2, 5, 6, 9, 12, 19, 22, 25, 28, 35, 40, 47, 56, 73
Offset: 0

Views

Author

Omar E. Pol, Jun 21 2009

Keywords

Comments

The sequence gives the number of Y-toothpicks in the structure after n rounds. A160123 (the first differences) gives the number added at the n-th round.
See the entries A160120, A161830 and A161426 for more information about Y-toothpick sequences.

Links

Crossrefs

Cf. A160120, A160121, A160123, A160406, A161426, A161830, A161831.

Formula

a(n) = (A160120(n+1)-1)/3.
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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