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 1-5 of 5 results.

A194696 a(n) = 2*A194693(n).

Original entry on oeis.org

4, 4, 8, 12, 16, 16, 24, 26, 24, 20, 32, 40, 64, 40, 48, 54, 40, 20, 32, 48, 72, 82, 96, 96, 108, 68, 88, 100, 160, 96, 96, 110, 72, 20, 32, 48, 72, 82, 96, 108, 136, 124, 160, 160, 248, 190, 208, 178, 188, 88, 96, 136
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

Conjecture: number of toothpicks or D-toothpicks added to the structure of A194440 at stage 2^k+n, if k tends to infinity. It appears that rows of A194441 when written as a triangle converge to this sequence.

Examples

			Written as a triangle:
4,
4,
8,
12,16,
16,24,26,24,
20,32,40,64,40,48,54,40,
20,32,48,72,82,96,96,108,68,88,100,160,96,96,110,72,
20,32,48,72,82,96,108,136,124,160,160,248,190,208,178,...

Links

Crossrefs

Cf. A152980, A194270, A194440, A194692, A194693, A194697.

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.

A194441 Number of toothpicks or D-toothpicks added at n-th stage to the structure of A194440.

Original entry on oeis.org

0, 1, 2, 4, 4, 4, 4, 8, 8, 4, 4, 8, 12, 16, 8, 16, 16, 4, 4, 8, 12, 16, 16, 24, 26, 24, 12, 20, 28, 40, 20, 32, 32, 4, 4, 8, 12, 16, 16, 24, 26, 24, 20, 32, 40, 64, 40, 48, 54, 40, 12, 20, 32, 48, 48, 64, 70, 76, 30, 44, 64, 88, 44, 64, 64, 4, 4, 8, 12
Offset: 0

Views

Author

Omar E. Pol, Aug 29 2011

Keywords

Comments

Essentially the first differences of A194440.

Examples

			If written as a triangle:
0,
1,
2,
4,4,
4,4,8,8,
4,4,8,12,16,8,16,16,
4,4,8,12,16,16,24,26,24,12,20,28,40,20,32,32,
4,4,8,12,16,16,24,26,24,20,32,40,64,40,48,54,40,12,20,...
.
It appears that rows converge to A194696.

Links

Crossrefs

Cf. A139251, A160121, A160407, A161831, A194271, A194440, A194443, A194445, A194692, A194693, A194696.

Formula

Conjectures for n = 2^k+j, if -1<=j<=3:
a(2^k-1) = 2^k, if k >= 2.
a(2^k+0) = 2^k, if k >= 0.
a(2^k+1) = 4, if k >= 1.
a(2^k+2) = 4, if k >= 1.
a(2^k+3) = 8, if k >= 2.
End of conjectures.

Extensions

More terms from Omar E. Pol, Dec 28 2012

A194692 Corner sequence associated with A194440 and A194441.

Original entry on oeis.org

0, 2, 4, 8, 14, 22, 30, 42, 55, 67, 77, 93, 113, 145, 165, 189, 216, 236, 246, 262, 286, 322, 363, 411, 459, 513, 547, 591, 641, 721, 769, 817, 872, 908, 918, 934, 958, 994, 1035, 1083, 1137, 1205, 1267, 1347, 1427, 1551, 1646, 1750, 1839, 1933, 1977, 2025, 2093
Offset: 0

Views

Author

Omar E. Pol, Sep 01 2011

Keywords

Comments

The sequence gives the number of toothpicks and D-toothpicks after n-th stage in the D-toothpick "corner" structure related to the D-toothpick "wide" triangle (See A194440). The first differences (A194693) give the number of toothpicks or D-toothpicks added at n-th stage.

Links

Crossrefs

Cf. A153006, A170883, A194270, A194440, A194441, A194694.

A194695 Number of toothpicks or D-toothpicks added at n-th stage to the D-toothpick "corner" structure of A194694.

Original entry on oeis.org

2, 2, 4, 6, 8, 8, 11, 16, 13, 10, 12, 20, 22, 26, 24, 36, 21, 10, 12
Offset: 1

Views

Author

Omar E. Pol, Sep 03 2011

Keywords

Comments

Sequence related to the D-toothpick "narrow" triangle (See A194442 and A194443). First differences of A194694.

Examples

			Written as a triangle:
2,
2,
4,
6,8,
8,11,16,13,
10,12,20,22,26,24,36,21,
10,12

Links

Crossrefs

Cf. A152980, A194271, A194442, A194443, A194693, A194694, A194697

Formula

a(n) = A194697(n)/2.
Showing 1-5 of 5 results.

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