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 11-13 of 13 results.

A223842 Number of 6 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

7, 49, 232, 824, 2388, 5992, 13582, 28642, 57306, 110164, 205131, 371923, 658926, 1143584, 1947904, 3261320, 5374024, 8725020, 13970658, 22081342, 34476575, 53211615, 81232894, 122724138, 183570978, 271978936, 399288201, 581038793, 838351784, 1199706462, 1703209968
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Examples

			Some solutions for n=3:
..0..1..0....0..0..0....0..0..0....0..0..0....1..1..0....0..0..0....0..0..0
..0..1..0....1..0..0....0..0..0....0..0..0....1..1..0....0..0..0....0..0..0
..0..1..0....1..0..0....0..0..1....0..0..0....1..1..0....0..1..0....0..0..0
..0..1..0....1..1..0....0..1..1....0..0..0....1..1..0....0..1..1....1..0..0
..0..1..0....1..1..1....1..1..1....0..0..0....1..1..1....1..1..1....1..1..0
..1..1..0....1..1..1....1..1..1....0..1..1....1..1..1....1..1..1....1..1..1

Links

Crossrefs

Row 6 of A223838.

Formula

Empirical: a(n) = (1/479001600)*n^12 - (1/15966720)*n^11 + (13/6220800)*n^10 - (1/53760)*n^9 + (6631/14515200)*n^8 + (125/96768)*n^7 - (1017767/43545600)*n^6 + (1429367/1451520)*n^5 - (7479853/1555200)*n^4 + (4300223/120960)*n^3 - (151629803/1663200)*n^2 - (12136/231)*n + 528 for n>6.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A223843 Number of 7 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

8, 64, 342, 1356, 4325, 11749, 28369, 62869, 130891, 260219, 499470, 932402, 1701094, 3042926, 5348741, 9253153, 15773146, 26518532, 44008367, 72142211, 116895662, 187337832, 297106834, 466531024, 725652569, 1118500677, 1709080380, 2589696200, 3892426882, 5804817830
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Examples

			Some solutions for n=3:
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..0..1....1..0..0
..0..0..0....1..0..0....0..0..0....0..0..0....0..1..0....0..0..1....1..0..0
..0..1..0....1..1..0....1..0..0....0..0..0....0..1..0....0..0..1....1..1..0
..0..1..0....1..1..0....1..1..0....0..0..0....0..1..1....0..0..1....1..1..0
..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..0
..0..1..0....1..1..0....1..1..0....1..1..0....1..1..1....0..1..1....1..1..1
..0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1....1..1..1

Links

Crossrefs

Row 7 of A223838.

Formula

Empirical: a(n) = (1/87178291200)*n^14 - (1/1779148800)*n^13 + (1/45619200)*n^12 - (53/136857600)*n^11 + (137/17418240)*n^10 - (1229/29030400)*n^9 + (739771/609638400)*n^8 - (1517923/87091200)*n^7 + (321517/691200)*n^6 - (12905723/3110400)*n^5 + (4378639787/119750400)*n^4 - (369357239/2494800)*n^3 + (61973609597/151351200)*n^2 - (519380551/360360)*n + 3759 for n>8.

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025

A223832 Number of n X n 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

Original entry on oeis.org

1, 2, 9, 48, 249, 1240, 5992, 28369, 132427, 611901, 2805670, 12786249, 57979474, 261797013, 1177774158, 5281497918
Offset: 0

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Examples

			Some solutions for n=3:
..0..1..0....0..0..0....1..1..0....0..0..1....0..0..0....1..1..1....0..0..0
..0..1..1....1..0..0....1..1..0....0..0..1....0..1..0....1..1..1....0..1..0
..1..1..1....1..1..1....1..1..1....0..1..1....0..1..0....1..1..1....0..1..1

Crossrefs

Main diagonal of A223838.

Extensions

a(0)=1 prepended by Alois P. Heinz, Feb 14 2024
Name corrected by Andrew Howroyd, Mar 18 2025
Previous Showing 11-13 of 13 results.

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