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 1-10 of 10 results.

A195797 Number of triangular nXnXn 0..n arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 4, 125, 5052, 5828215, 479534519840
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Diagonal of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....0.1........5.0........5.0........4.3........5.0........1.0........3.2
....4.4.3......5.0.5......3.0.5......4.0.3......3.0.4......3.1.3......5.1.5
...1.2.3.1....0.0.0.5....0.4.2.3....2.1.2.4....0.2.1.4....0.1.1.1....1.4.4.2
..0.0.5.0.0..0.5.5.0.0..0.5.1.2.0..0.5.2.3.0..0.5.2.1.0..0.1.3.0.0..0.4.2.3.0

A195798 Number of triangular n X n X n 0..1 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 2, 8, 16, 64, 1184, 5300, 130324, 14748808, 421963232, 54990266540
Offset: 1

Views

Author

R. H. Hardin, Sep 23 2011

Keywords

Comments

From Pontus von Brömssen, Sep 08 2022: (Start)
For n <= 6, all solutions are rotationally symmetric, which implies that a(n) = 2^(A007997(n+4)-1). But for n >= 7 there exist asymmetric solutions like
0
0 0
0 0 1
0 1 0 0
1 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0 0.
(End)

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....0.0........0.0........0.0........0.1........0.1........0.1........0.1
....0.1.0......1.0.1......1.1.1......0.0.0......0.1.0......1.0.1......1.1.1
...0.1.1.0....0.0.0.0....0.1.1.0....1.0.0.0....1.1.1.0....1.0.0.0....1.1.1.0
..0.0.0.0.0..0.0.1.0.0..0.0.1.0.0..0.0.0.1.0..0.0.0.1.0..0.0.1.1.0..0.0.1.1.0

Crossrefs

Column 1 of A195805.
Cf. A007997.

A195806 Number of triangular of a 5 X 5 X 5 0..n arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

16, 105, 496, 1759, 5052, 12469, 27412, 55059, 102952, 181543, 304908, 491563, 765184, 1155567, 1699684, 2442553, 3438468, 4752283, 6460432, 8652429, 11432392, 14920189, 19253232, 24588229, 31102456, 38995845, 48492976, 59844451, 73329300
Offset: 1

Views

Author

R. H. Hardin, Sep 23 2011

Keywords

Examples

			Some solutions for n=4:
      0          0          0          0          0          0          0
     0 1        2 2        1 1        1 4        4 2        4 1        0 0
    2 0 2      1 0 4      0 3 0      4 2 0      2 4 2      1 0 4      3 2 3
   1 0 0 0    3 3 0 0    1 3 3 1    2 0 4 3    2 4 4 4    2 3 0 2    0 2 2 0
  0 0 2 1 0  0 1 1 4 0  0 1 0 1 0  0 3 2 2 0  0 4 2 2 0  0 3 1 3 0  0 0 3 0 0

Links

Crossrefs

Row 5 of A195805.

Formula

From Manuel Kauers and Christoph Koutschan, Mar 01 2023: (Start)
Conjectured recurrence: a(n) - 3*a(n+1) + 2*a(n+2) - a(n+3) + 6*a(n+4) - 5*a(n+5) - 3*a(n+6) + 3*a(n+8) + 5*a(n+9) - 6*a(n+10) + a(n+11) - 2*a(n+12) + 3*a(n+13) - a(n+14) = 0.
Conjectured closed form as a quasi-polynomial:
a(6*n) = 1 + 25*n + 158*n^2 + 650*n^3 + 2275*n^4 + 4680*n^5 + 4680*n^6.
a(6*n+1) = 16 + 198*n + 1133*n^2 + 3900*n^3 + 8125*n^4 + 9360*n^5 + 4680*n^6.
a(6*n+2) = 105 + 1087*n + 4922*n^2 + 12350*n^3 + 17875*n^4 + 14040*n^5 + 4680*n^6.
a(6*n+3) = 496 + 4148*n + 14783*n^2 + 28600*n^3 + 31525*n^4 + 18720*n^5 + 4680*n^6.
a(6*n+4) = 1759 + 12121*n + 35258*n^2 + 55250*n^3 + 49075*n^4 + 23400*n^5 + 4680*n^6.
a(6*n+5) = (1+n)^2*(5052 + 19370*n + 28405*n^2 + 18720*n^3 + 4680*n^4). (End)

A195799 Number of triangular nXnXn 0..2 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 3, 27, 105, 1695, 284427, 11606931
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 2 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....1.0........1.0........1.1........1.2........0.0........1.2........2.0
....1.0.1......2.0.2......2.2.2......0.1.0......2.0.2......0.1.0......1.1.1
...0.0.0.1....0.0.0.1....1.2.2.1....2.1.1.1....0.0.0.0....2.1.1.1....0.1.1.2
..0.1.1.0.0..0.1.2.0.0..0.1.2.1.0..0.1.0.2.0..0.0.2.0.0..0.1.0.2.0..0.2.1.0.0

A195800 Number of triangular nXnXn 0..3 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 4, 64, 496, 24928, 17528896, 3850960912
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 3 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....3.3........1.0........2.0........2.2........1.0........0.1........2.0
....0.3.0......1.1.3......3.0.3......1.0.1......1.1.1......0.2.0......3.0.3
...3.3.3.3....1.2.0.0....0.0.0.2....2.0.0.2....0.1.1.1....1.2.2.0....0.0.0.2
..0.3.0.3.0..0.0.2.1.0..0.2.3.0.0..0.2.1.2.0..0.1.1.0.0..0.0.0.1.0..0.2.3.0.0

A195801 Number of triangular nXnXn 0..4 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 5, 125, 1759, 213319
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 4 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....2.2........3.0........1.3........4.2........4.2........2.1........0.2
....2.2.0......1.3.1......0.1.0......0.3.2......0.3.3......2.2.0......3.4.2
...1.1.3.3....0.3.3.3....3.1.1.1....3.4.2.3....4.3.0.3....0.1.3.3....2.2.3.1
..0.3.1.1.0..0.3.1.0.0..0.1.0.3.0..0.3.1.3.0..0.2.3.3.0..0.3.1.0.0..0.0.4.1.0

A195802 Number of triangular nXnXn 0..5 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 6, 216, 5052, 1274808, 6711447312
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 5 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....4.3........4.3........1.2........3.2........5.4........2.1........4.5
....4.4.3......4.2.3......5.5.2......1.4.0......3.5.4......4.0.5......2.1.1
...3.2.3.5....3.0.1.5....1.2.5.3....2.2.3.4....5.4.3.5....1.2.1.1....4.2.3.4
..0.4.5.2.0..0.4.5.2.0..0.2.5.0.0..0.3.2.1.0..0.4.5.4.0..0.2.3.2.0..0.5.0.5.0

A195803 Number of triangular nXnXn 0..6 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 7, 343, 12469, 5828215
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 6 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....3.6........4.1........2.5........1.6........0.5........0.6........1.2
....1.4.0......3.5.1......5.0.3......1.4.0......1.1.1......2.2.2......0.2.0
...6.2.3.4....0.4.6.5....3.2.4.2....6.2.3.2....5.1.1.0....6.2.2.0....2.2.2.1
..0.3.2.5.0..0.5.2.0.0..0.4.1.5.0..0.1.2.5.0..0.0.1.5.0..0.0.2.6.0..0.1.0.2.0

A195804 Number of triangular nXnXn 0..7 arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

1, 1, 8, 512, 27412, 21779968, 479534519840
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Column 7 of A195805

Examples

			Some solutions for n=5
......0..........0..........0..........0..........0..........0..........0
.....1.1........4.0........1.1........2.5........3.0........3.0........6.3
....0.1.2......0.1.2......0.1.2......7.1.2......5.1.6......5.1.6......1.1.2
...2.2.0.0....1.2.0.3....2.2.0.0....2.0.5.4....0.3.2.2....0.3.2.2....3.3.2.5
..0.0.1.2.0..0.3.1.1.0..0.0.1.2.0..0.5.3.3.0..0.3.4.1.0..0.3.4.1.0..0.6.0.4.0

A195807 Number of triangular of a 6X6X6 0..n arrays with all rows and diagonals having the same length having the same sum, with corners zero.

Original entry on oeis.org

64, 1695, 24928, 213319, 1274808, 5828215, 21779968
Offset: 1

Views

Author

R. H. Hardin Sep 23 2011

Keywords

Comments

Row 6 of A195805

Examples

			Some solutions for n=3
.......0............0............0............0............0............0
......1.2..........0.1..........3.3..........1.2..........0.1..........0.3
.....3.1.2........0.2.0........0.3.1........3.1.2........0.2.0........2.2.2
....3.1.0.3......1.1.1.0......3.0.0.2......3.1.0.3......1.1.1.0......2.3.3.2
...1.0.2.2.1....1.0.1.1.1....3.0.3.0.3....1.0.2.2.1....1.0.1.1.1....3.2.3.2.0
..0.2.3.1.2.0..0.0.1.1.0.0..0.3.1.2.3.0..0.2.3.1.2.0..0.0.1.1.0.0..0.0.2.2.3.0
Showing 1-10 of 10 results.

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