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.

A222955 Number of nX1 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope.

Original entry on oeis.org

2, 2, 4, 4, 8, 8, 20, 18, 52, 48, 152, 138, 472, 428, 1520, 1392, 5044, 4652, 17112, 15884, 59008, 55124, 206260, 193724, 729096, 688008, 2601640, 2465134, 9358944, 8899700, 33904324, 32342236, 123580884, 118215780, 452902072, 434314138, 1667837680
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2013

Keywords

Comments

Column 1 of A222959
Conjecture: A binary word is counted iff it has the same sum of positions of 1's as its reverse, or, equivalently, the same sum of partial sums as its reverse. - Gus Wiseman, Jan 07 2023

Examples

			All solutions for n=4
..0....1....1....0
..0....1....0....1
..0....1....0....1
..0....1....1....0
From _Gus Wiseman_, Jan 07 2023: (Start)
The a(1) = 2 through a(7) = 20 binary words with least squares fit a line of zero slope are:
  (0)  (00)  (000)  (0000)  (00000)  (000000)  (0000000)
  (1)  (11)  (010)  (0110)  (00100)  (001100)  (0001000)
             (101)  (1001)  (01010)  (010010)  (0010100)
             (111)  (1111)  (01110)  (011110)  (0011100)
                            (10001)  (100001)  (0100010)
                            (10101)  (101101)  (0101010)
                            (11011)  (110011)  (0110001)
                            (11111)  (111111)  (0110110)
                                               (0111001)
                                               (0111110)
                                               (1000001)
                                               (1000110)
                                               (1001001)
                                               (1001110)
                                               (1010101)
                                               (1011101)
                                               (1100011)
                                               (1101011)
                                               (1110111)
                                               (1111111)
(End)

Links

Crossrefs

These words appear to be ranked by A359402.
A011782 counts compositions.
A359042 adds up partial sums of standard compositions, reversed A029931.
Cf. A053632, A070925, A231204, A318283, A359043.

A222956 Number of nX3 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope.

Original entry on oeis.org

4, 4, 16, 16, 64, 64, 400, 324, 2704, 2304, 23104, 19044, 222784, 183184, 2310400, 1937664, 25441936, 21641104, 292820544, 252301456, 3481944064, 3038655376, 42543187600, 37528988176, 531580977216, 473355008064, 6768530689600
Offset: 1

Views

Author

R. H. Hardin Mar 10 2013

Keywords

Comments

Column 3 of A222959

Examples

			Some solutions for n=4
..1..0..1....0..0..0....1..1..1....1..0..1....1..0..1....0..0..0....1..0..1
..0..0..0....0..1..0....1..1..1....1..1..1....1..0..1....0..0..0....0..1..0
..0..0..0....0..1..0....1..1..1....1..1..1....1..0..1....0..0..0....0..1..0
..1..0..1....0..0..0....1..1..1....1..0..1....1..0..1....0..0..0....1..0..1

Links

A222957 Number of nX5 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope.

Original entry on oeis.org

8, 8, 64, 64, 512, 512, 8000, 5832, 140608, 110592, 3511808, 2628072, 105154048, 78402752, 3511808000, 2697228288, 128329125184, 100674415808, 5010745148928, 4007556327104, 205462555328512, 167502838946624, 8774957874376000
Offset: 1

Views

Author

R. H. Hardin Mar 10 2013

Keywords

Comments

Column 5 of A222959

Examples

			Some solutions for n=4
..0..1..1..1..0....1..1..1..1..1....0..0..1..0..0....0..0..0..0..0
..0..1..0..1..0....0..1..0..1..0....1..1..1..1..1....0..1..0..1..0
..0..1..0..1..0....0..1..0..1..0....1..1..1..1..1....0..1..0..1..0
..0..1..1..1..0....1..1..1..1..1....0..0..1..0..0....0..0..0..0..0

Links

A222954 Number of n X n 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope.

Original entry on oeis.org

2, 2, 16, 16, 512, 512, 323600, 144930, 1808243216, 615667968
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2013

Keywords

Examples

			Some solutions for n=4
..0..1..1..0....1..1..1..1....0..0..0..0....1..0..0..1....0..1..1..0
..1..1..1..1....1..0..0..1....1..1..1..1....0..1..1..0....1..0..0..1
..1..1..1..1....1..0..0..1....1..1..1..1....0..1..1..0....1..0..0..1
..0..1..1..0....1..1..1..1....0..0..0..0....1..0..0..1....0..1..1..0

Crossrefs

Main diagonal of A222959.

A222958 Number of nX7 0..1 arrays with every row and column least squares fitting to a zero slope straight line, with a single point array taken as having zero slope.

Original entry on oeis.org

20, 20, 400, 400, 8000, 8000, 323600, 215892, 14843920, 9734400, 1138729280, 631004724, 117308595520, 59768363024, 14742894291200, 7399937947392, 2167430898315280, 1074761911462928, 361218009407664960
Offset: 1

Views

Author

R. H. Hardin Mar 10 2013

Keywords

Comments

Column 7 of A222959

Examples

			Some solutions for n=4
..1..1..1..0..1..1..1....0..0..1..0..1..0..0....0..1..1..1..0..0..1
..0..0..1..1..1..0..0....0..1..1..0..0..0..1....0..0..1..1..1..0..0
..0..0..1..1..1..0..0....0..1..1..0..0..0..1....0..0..1..1..1..0..0
..1..1..1..0..1..1..1....0..0..1..0..1..0..0....0..1..1..1..0..0..1
Showing 1-5 of 5 results.

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