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 1-4 of 4 results.

A347676 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k that contain the maximal number of 1's.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 12, 26, 12, 1, 1, 16, 55, 55, 16, 1, 1, 20, 96, 156, 96, 20, 1, 1, 24, 149, 354, 354, 149, 24, 1, 1, 28, 214, 688, 1037, 688, 214, 28, 1, 1, 32, 291, 1198, 2533, 2533, 1198, 291, 32, 1, 1, 36, 380, 1924, 5383, 7632, 5383, 1924, 380, 36, 1
Offset: 1

Views

Author

N. J. A. Sloane, Sep 10 2021

Keywords

Examples

			The array begins:
1,1,1,1,1,1,1, ...
1,4,8,12,16,20,24, ...
1,8,26,55,96,149,214, ...
1,12,55,156,354,688,1198, ...
1,16,96,354,1037,2533,5383, ...
1,20,149,688,2533,7632,19522, ...
1,24,214,1198,5383,19522,59020, ...
...
The first few antidiagonals are:
1,
1,1,
1,4,1,
1,8,8,1,
1,12,26,12,1,
1,16,55,55,16,1,
1,20,96,156,96,20,1,
1,24,149,354,354,149,24,1,
1,28,214,688,1037,688,214,28,1,
...

Links

Crossrefs

Cf. A347672, A347675.
Row 3 is A347677.

Formula

a(n) <= A347672(n). - Michael S. Branicky, Sep 15 2021

Extensions

a(45)-a(66) from Michael S. Branicky, Sep 14 2021

A347673 Number of Baxter matrices of size 3 X n.

Original entry on oeis.org

1, 14, 69, 203, 463, 903, 1585, 2579, 3963, 5823, 8253, 11355, 15239, 20023, 25833, 32803, 41075, 50799, 62133, 75243, 90303, 107495, 127009, 149043, 173803, 201503, 232365, 266619, 304503, 346263, 392153, 442435, 497379, 557263, 622373, 693003, 769455, 852039
Offset: 1

Views

Author

N. J. A. Sloane, Sep 10 2021

Keywords

Links

Crossrefs

Row 3 of A347672.

Programs

  • Mathematica
    Rest@ CoefficientList[Series[-x (x^6 - 3 x^5 + 3 x^4 - 12 x^3 + 9 x^2 + 9 x + 1)/(x - 1)^5, {x, 0, 38}], x] (* Michael De Vlieger, Oct 20 2021 *)

Formula

From George Spahn, Oct 20 2021: (Start)
a(n) = 1/3*n^4 + 3*n^3 - 16/3*n^2 + 2*n + 3 for n >= 3.
G.f.: -x*(x^6 - 3*x^5 + 3*x^4 - 12*x^3 + 9*x^2 + 9*x + 1)/(x - 1)^5. (End)

Extensions

a(8)-a(38) from Michael S. Branicky, Sep 13 2021

A347675 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k that contain the minimal number of 1's.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 6, 12, 1, 1, 20, 32, 32, 20, 1, 1, 30, 100, 22, 100, 30, 1, 1, 42, 240, 172, 172, 240, 42, 1, 1, 56, 490, 744, 92, 744, 490, 56, 1, 1, 72, 896, 2364, 956, 956, 2364, 896, 72, 1, 1, 90, 1512, 6174, 5328, 422, 5328, 6174, 1512, 90, 1
Offset: 1

Views

Author

N. J. A. Sloane, Sep 10 2021

Keywords

Examples

			The array begins:
1,1,1,1,1,1,1,...
1,2,6,12,20,30,42,...
1,6,6,32,100,240,490,...
1,12,32,22,172,744,2364,...
1,20,100,172,92,956,5328,...
1,30,240,744,956,422,5492,...
1,42,490,2364,5328,5492,2074,...
...
The first few antidiagonals are:
1,
1,1,
1,2,1,
1,6,6,1,
1,12,6,12,1,
1,20,32,32,20,1,
1,30,100,22,100,30,1,
1,42,240,172,172,240,42,1,
1,56,490,744,92,744,490,56,1,
...

Links

Crossrefs

Cf. A347672, A347676.
The main diagonal is A001181.

Formula

a(n) <= A347672(n). - Michael S. Branicky, Sep 15 2021

Extensions

a(46)-a(66) from Michael S. Branicky, Sep 14 2021

A347674 Number of Baxter matrices of size n X n.

Original entry on oeis.org

1, 6, 69, 972, 16355, 306352, 6175181
Offset: 1

Views

Author

N. J. A. Sloane, Sep 10 2021

Keywords

Crossrefs

Main diagonal of A347672.

Extensions

a(4) corrected by Michael S. Branicky, Sep 15 2021
Showing 1-4 of 4 results.

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

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