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.

Previous Showing 41-49 of 49 results.

A159794 a(n) = A153006(n)*3.

Original entry on oeis.org

0, 3, 9, 18, 27, 39, 60, 84, 99, 111, 132, 159, 189, 234, 300, 360, 387, 399, 420, 447, 477, 522, 588, 651, 693, 738, 807, 891, 996, 1152, 1344, 1488, 1539, 1551, 1572, 1599, 1629, 1674, 1740, 1803, 1845, 1890, 1959, 2043, 2148, 2304, 2496, 2643
Offset: 0

Views

Author

Omar E. Pol, May 02 2009

Keywords

Links

Crossrefs

Toothpick sequence: A139250.
Cf. A139251, A152980, A153006, A159793, A159795.

Extensions

More terms from Max Alekseyev, Dec 13 2011

A161427 First differences of A161426.

Original entry on oeis.org

1, 3, 3, 7, 5, 7, 9, 17, 11, 7
Offset: 1

Views

Author

Omar E. Pol and David Applegate, Jun 20 2009

Keywords

Comments

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

Links

Crossrefs

Cf. A139251, A152980, A160121, A161426, A161831.

A162777 a(n) = A153003(n) - A153006(n).

Original entry on oeis.org

0, 0, 1, 1, 1, 3, 5, 3, 1, 3, 5, 5, 7, 13, 15, 7, 1, 3, 5, 5, 7, 13, 15, 9, 7, 13, 17, 19, 29, 43, 39, 15, 1, 3, 5, 5, 7, 13, 15, 9, 7, 13, 17, 19, 29, 43, 39, 17, 7, 13, 17, 19, 29, 43, 41, 27, 29, 45, 55, 69, 103, 127, 95, 31
Offset: 0

Views

Author

Omar E. Pol, Jul 23 2009

Keywords

Comments

The main entry for this sequence is the toothpick sequence A139250.

Examples

			If written as a triangle:
0;
0;
1,1;
1,3,5,3;
1,3,5,5,7,13,15,7;
1,3,5,5,7,13,15,9,7,13,17,19,29,43,39,15;
...
Rows converge to A162779.

Links

Crossrefs

Cf. A139250, A152980, A153003, A153004, A153006, A162779.

Formula

Observation: It appears that a(2^i) = 1, i > 0 and a(2^i-1) = 2^(i-1) - 1, i > 0.

Extensions

More terms from Jinyuan Wang, Mar 15 2020

A161211 First differences of A161210.

Original entry on oeis.org

1, 2, 4, 7, 7, 7
Offset: 1

Views

Author

Omar E. Pol, Jun 06 2009

Keywords

Comments

Number of toothpicks added at the n-th round.

Links

Crossrefs

Cf. A139251, A152980, A160161, A161210, A161213, A161215, A161217.

A161417 First differences of A160416.

Original entry on oeis.org

1, 7, 3, 21, 7, 41, 9, 57, 13
Offset: 1

Views

Author

Omar E. Pol, May 20 2009, Jun 14 2009

Keywords

Links

Crossrefs

Cf. A139250, A139251, A153006, A152980, A160411, A160413, A160415, A160416.
Cf. A160797.

A182837 Number of toothpick added at n-th stage to the toothpick structure of A182836.

Original entry on oeis.org

0, 1, 2, 4, 8, 12, 12, 12, 20, 20, 16, 20
Offset: 0

Views

Author

Omar E. Pol, Dec 12 2010

Keywords

Comments

First differences of A182836.

Links

Crossrefs

Cf. A139250, A139251, A152980, A182633, A182635, A182836, A182841.

A194811 Number of grid points that are covered after n-th stage of A139250 version "Tree", starting with a(0) = 1 and assuming the toothpicks have length 4, 3, and 2.

Original entry on oeis.org

1, 5, 13, 25, 37, 53, 81, 113, 133, 149, 177, 213, 253, 313, 401, 481, 517, 533, 561, 597, 637, 697, 785, 869, 925, 985, 1077, 1189, 1329, 1537, 1793, 1985, 2053, 2069, 2097, 2133, 2173, 2233, 2321, 2405, 2461, 2521, 2613, 2725, 2865, 3073, 3329, 3525, 3613
Offset: 0

Views

Author

Omar E. Pol, Oct 24 2011

Keywords

Comments

The first differences give A147646.

Links

Crossrefs

Cf. A139250, A152980, A153006, A147646, A159795, A160128, A160420, A160422, A160425, A182618, A194800, A194802.

Formula

a(n) = 1 + 4*A153006(n) = 1 + A159795(n).

A159801 Partial sums of A153001.

Original entry on oeis.org

4, 11, 20, 30, 45, 67, 88, 102, 117, 140, 168, 203, 255, 319, 368, 390, 405, 428, 456, 491, 543, 608, 664, 707, 760, 834, 925, 1047, 1215, 1391, 1504, 1542, 1557, 1580, 1608, 1643, 1695, 1760, 1816, 1859, 1912, 1986, 2077, 2199, 2367, 2544, 2664, 2723, 2776, 2850
Offset: 1

Views

Author

Omar E. Pol, May 18 2009

Keywords

Links

Crossrefs

Cf. A139250, A139251, A152980, A153001, A153006.

Extensions

More terms from Jinyuan Wang, Mar 15 2020

A220499 Number of line segments in an H tree with n levels that have no correspondence with the toothpicks of the toothpick structure of A139250 after n-th stage.

Original entry on oeis.org

0, 0, 0, 0, 4, 16, 40, 92, 212, 464, 968, 1980, 4016, 8096, 16260, 32612, 65364, 130896, 261960, 524092, 1048368, 2096928, 4194052, 8388324, 16776912, 33554112, 67108516, 134217344, 268435032, 536870428, 1073741252, 2147482996, 4294966612, 8589933904
Offset: 0

Views

Author

Omar E. Pol, Feb 16 2013

Keywords

Comments

More generally, differences between A000225 and A139250.

Examples

			For n = 0..3, the number of line segments in the H tree equals the number of toothpicks in the toothpick structure of A139250, so a(n) = 0, if 0 <= n <= 3. Note that there is a correspondence between every element from the two structures. For n = 4 the H tree contains 15 line segments, on the other hand the toothpick structure contains only 11 toothpicks. There are four line segments in the H tree that have no correspondence with the toothpicks of the toothpicks structure. They are the four line segments of the last generation that are closer to the center of the H tree, so a(4) = 4.

Links

Crossrefs

Cf. A000079, A000225, A139250, A139251, A152978, A152980, A153000, A153006.

Formula

a(n) = A000225(n) - A139250(n).
Previous Showing 41-49 of 49 results.

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