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.

A141731 Numbers of 1's in the rows of triangle A141728.

Original entry on oeis.org

1, 0, 3, 2, 4, 3, 6, 9, 7, 7, 9, 8, 11, 8, 13, 16, 18, 14, 14, 14, 22, 20, 20, 25, 22, 23, 24, 17, 29, 22, 29, 36, 38, 34, 32, 32, 38, 36, 34, 36, 36, 40, 44, 44, 34, 30, 42, 45, 50, 45, 38, 43, 49, 50, 55, 56, 58, 62, 56, 49, 58, 51, 62, 71, 73, 65, 65, 63, 69, 69, 69, 67, 67, 75
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Crossrefs

Cf. A141727 - A141730, A141732 - A141746.

A141732 Numbers of 0's in the rows of triangle A141728.

Original entry on oeis.org

0, 3, 2, 5, 5, 8, 7, 6, 10, 12, 12, 15, 14, 19, 16, 15, 15, 21, 23, 25, 19, 23, 25, 22, 27, 28, 29, 38, 28, 37, 32, 27, 27, 33, 37, 39, 35, 39, 43, 43, 45, 43, 41, 43, 55, 61, 51, 50, 47, 54, 63, 60, 56, 57, 54, 55, 55, 53, 61, 70, 63, 72, 63, 56, 56, 66, 68, 72, 68, 70, 72, 76
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Crossrefs

Cf. A141727 - A141731, A141733 - A141746.

A141734 Binary digits, representing the rows of triangle A141728, written in base 10.

Original entry on oeis.org

1, 0, 21, 24, 293, 7, 5452, 6637, 74664, 6458, 1384558, 1578150, 19209993, 474240, 357331029, 434949016, 4893636133, 421910023, 90731484851, 103435736251, 1258858815339, 30658739531, 23416607110667, 28506443273867
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Crossrefs

Cf. A141727 - A141733, A141735 - A141746.

A141737 List of the 0's and 1's digits of triangle A141728 along a boustrophedon path. First case: see example below.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Examples

			First boustrophedon path:
................................/1.
.............................../_____
...............................0.0.0.\
............................._________\
.........................../.1.0.1.0.1.
.........................../______________
...........................0.0.1.1.0.0.0.\
.........................__________________\
......................./.1.0.0.1.0.0.1.0.1
......................./_____________________
.......................0.0.0.0.0.0.0.0.1.1.1

Crossrefs

Cf. A141727 - A141736, A141738 - A141746.

A141738 List of the 0's and 1's digits of triangle A141728 along a boustrophedon path. Second case: see example below.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Examples

			Second boustrophedon path:
.................................1\
...............................____\
............................../0.0.0.
............................./________
.............................1.0.1.0.1\
............................___________\
........................../0.0.1.1.0.0.0
........................./________________
.........................1.0.0.1.0.0.1.0.1\
........................___________________\
.......................0.0.0.0.0.0.0.0.1.1.1

Crossrefs

Cf. A141727 - A141737, A141739 - A141746.

A141740 Cumulative sum of the rows of triangle A141728.

Original entry on oeis.org

1, 1, 4, 6, 10, 13, 19, 28, 35, 42, 51, 59, 70, 78, 91, 107, 125, 139, 153, 167, 189, 209, 229, 254, 276
Offset: 0

Views

Author

Paolo P. Lava, Jul 03 2008

Keywords

Crossrefs

Cf. A141727 - A141739, A141741 - A141746.
Cf. A141727 - A141739, A141741 - A141746.

A141742 Starting from the 1 in the first line of triangle A141728 choose one of the three digits below it. Repeat down to the other rows. Sequence gives the numbers in base 10 expressed by the collected digits that cannot be reached following any possible path.

Original entry on oeis.org

3, 6, 7, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30
Offset: 0

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 07 2008

Keywords

Examples

			Below the 1 in the first row we have three 0. Therefore we cannot have "11", 3 in base 10.

Crossrefs

Cf. A004755, A141727 - A141741, A141743 - A141746.

A141727 Triangle T(n,k) read by rows. Entries are 0 and 1. Start with 1 in the top row, add a second row of 2n-1 elements (with n=2 -> 3). Moving from left to right add 0 if the number of adjacent 1's is even or add 1 if it is odd.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0
Offset: 0

Views

Author

Paolo P. Lava & Giorgio Balzarotti, Jul 02 2008

Keywords

Comments

Any diagonal, read top down from right to left, is a periodic sequence of 0's and 1's. The lengths of the periods are always powers of 2. Here are the periods for the first 20 diagonals:
1
0
10
10
0110
0
0100
1000
11110000
1110
01001110
00101000
01011100
1000
11100000
11001110
0111000110001110
01101000
0011011010011100
0010001010001000
If we draw a large number of rows we obtain an interesting figure with several large islands of zeros.

Examples

			.....................................1 First Row
...................................1 ... Add 1 to have an even number of adjacent 1's (2)
.....................................1 First Row
...................................1.0 ... Add 0 because there are two adjacent 1's (in the first and second rows)
......................................1 First Row
....................................1.0.1 ... Again add 1 to have an even number of adjacent 1's (2)
The second row is now complete.
.....................................1 First Row
...................................1.0.1 Second Row
.................................1 ... Add 1 because there is only an 1 adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0 ... Add 0 because there are two 1's adjacent (second and third row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0 ... Again add 0 because there are two 1's adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0.1 ... Add 1 because there is only an 1 adjacent (second row)
.....................................1 First Row
...................................1.0.1 Second Row
.................................1.0.0.1.0 ... Add 0 because there are two 1's adjacent (second and third row)
The third row is now complete. Then repeat the process for the other rows.
The triangle begins:
...........................1
........................1..0..1
.....................1..0..0..1..0
..................1..0..1..0..1..0..0
...............1..0..0..1..1..0..1..1..1
............1..0..1..0..0..0..0..0..1..1..0
.........1..0..0..1..0..0..0..0..1..1..1..0..0
......1..0..1..0..1..0..0..0..1..1..0..0..1..1..1
...1..0..0..1..1..0..1..1..0..0..0..1..0..0..1..1..0
1..0..1..0..0..0..0..0..0..1..1..0..1..0..1..1..1..0..0

Links

Crossrefs

Cf. A141728-A141746.

Extensions

Minor edits by N. J. A. Sloane, Sep 10 2012

A141729 Numbers of 1's in the rows of triangle A141727.

Original entry on oeis.org

1, 2, 3, 3, 6, 4, 5, 8, 8, 8, 8, 10, 9, 12, 12, 15, 18, 14, 16, 16, 16, 16, 18, 16, 17, 26, 20, 27, 24, 24, 25, 32, 32, 30, 30, 36, 28, 32, 36, 34, 26, 32, 28, 34, 30, 36, 36, 42, 33, 46, 42, 41, 38, 44, 41, 50, 42, 56, 44, 58, 45, 60, 52, 63, 66, 58, 62, 62, 52, 56, 64, 64, 46
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 02 2008

Keywords

Crossrefs

Cf. A141727, A141728, A141730 - A141746.
Showing 1-9 of 9 results.

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

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