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 13 results. Next

A209586 Number of n X n 0..1 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

2, 16, 192, 9216, 663552, 191102976, 82556485632, 142657607172096, 369768517790072832, 3833759992447475122176, 59622635402543133100081152, 3709004903121403223889848303616, 346094665520064377627609524907016192
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 1 of A209593

Examples

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

Links

Formula

a(n) = 2 ^ (2*n-(n modulo 2)) * 6 ^ ((n*n-2*n+(n modulo 2))/4)

A209585 Number of n X n 0..n arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

2, 81, 28672, 791015625, 191221621088256, 7860041410116536427241, 2836619246897071128576000000000, 304913968803300753908857213381006097576481
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Diagonal of A209593

Examples

			Some solutions for n=3
..0..0..1....3..0..2....2..0..1....0..3..0....2..0..0....3..3..3....0..2..2
..0..1..1....1..0..0....0..1..3....2..3..3....2..3..0....2..1..3....2..1..2
..3..1..2....0..1..1....1..3..3....3..2..2....2..2..3....0..2..0....0..2..3

Links

Formula

a(n) = (n+1) ^ (2n-(n modulo 2)) * ((n+1)*(2n+1)) ^ ((n*n-2n+(n modulo 2))/4)

A209587 Number of n X n 0..2 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

3, 81, 3645, 1476225, 996451875, 6053445140625, 61291132048828125, 5585154407949462890625, 848245325707324676513671875, 1159445329576199417209625244140625
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 2 of A209593

Examples

			Some solutions for n=3
..1..1..1....2..0..1....0..1..1....2..0..2....2..0..0....0..2..1....0..2..0
..1..2..2....0..1..2....1..2..1....2..1..0....0..0..0....2..1..0....1..1..2
..0..2..0....1..2..0....0..1..2....1..2..0....0..0..1....1..0..2....0..1..2

Links

Formula

a(n) = 3 ^ (2*n-(n modulo 2)) * 15 ^ ((n*n-2*n+(n modulo 2))/4)

A209588 Number of n X n 0..3 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

4, 256, 28672, 51380224, 161128382464, 8084777718513664, 709908161907247808512, 997369854092025849117147136, 2452157460147152961259796760100864
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 3 of A209593

Examples

			Some solutions for n=3
..3..0..2....2..0..1....0..2..0....3..3..1....0..3..0....0..2..3....2..3..0
..0..2..1....0..1..3....2..3..2....2..0..3....1..2..3....2..0..2....3..1..3
..2..1..0....3..3..2....1..2..1....3..2..3....3..1..3....0..2..1....3..3..0

Links

Formula

a(n) = 4 ^ (2*n-(n modulo 2)) * 28 ^ ((n*n-2*n+(n modulo 2))/4)

A209589 Number of n X n 0..4 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

5, 625, 140625, 791015625, 8009033203125, 2027286529541015625, 923682425022125244140625, 10521320122517645359039306640625, 215719941636994597502052783966064453125
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 4 of A209593

Examples

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

Links

Formula

a(n) = 5 ^ (2*n-(n modulo 2)) * 45 ^ ((n*n-2*n+(n modulo 2))/4)

A209590 Number of n X n 0..5 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

6, 1296, 513216, 7316407296, 191221621088256, 179919658395455717376, 310357092660359621536382976, 19272907305680273946696375374708736, 2194189968466526991277450769351996054962176
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 5 of A209593

Examples

			Some solutions for n=3
..0..5..4....0..2..3....3..2..3....0..4..1....0..3..2....0..0..3....0..0..2
..5..4..1....2..0..0....5..5..2....4..1..3....5..2..3....5..1..0....3..5..0
..2..1..5....3..0..1....2..5..0....3..3..5....4..5..1....5..5..5....4..3..3

Links

Formula

a(n) = 6 ^ (2*n-(n modulo 2)) * 66 ^ ((n*n-2*n+(n modulo 2))/4)

A209591 Number of n X n 0..6 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

7, 2401, 1529437, 47738317081, 2767247026234327, 7860041410116536427241, 41461694858240499304086993277, 10716805483614568896270487886484563281, 5144331626584186407654932265866559478676249287
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 6 of A209593

Examples

			Some solutions for n=3
..0..5..4....0..0..4....0..6..2....0..6..5....0..3..3....0..3..5....0..3..5
..5..2..1....0..3..2....6..0..2....5..2..6....3..5..0....2..2..3....3..5..5
..1..1..3....3..2..5....1..2..1....4..5..3....5..0..1....4..2..0....3..5..3

Links

Formula

a(n) = 7 ^ (2*n-(n modulo 2)) * 91 ^ ((n*n-2*n+(n modulo 2))/4)

A209592 Number of n X n 0..7 arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

8, 4096, 3932160, 241591910400, 27831388078080000, 205195258022068224000000, 2836619246897071128576000000000, 2509659166022727122011815936000000000000
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Column 7 of A209593

Examples

			Some solutions for n=3
..0..3..3....0..2..7....0..3..7....0..4..0....0..7..7....0..7..5....0..4..0
..3..2..7....2..5..5....3..5..3....6..7..4....7..1..2....4..6..7....1..0..4
..4..7..0....7..5..0....3..3..0....6..6..0....7..2..0....5..4..0....1..1..0

Links

Formula

a(n) = 8 ^ (2*n-(n modulo 2)) * 120 ^ ((n*n-2*n+(n modulo 2))/4)

A209594 Number of 3 X 3 0..n arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

192, 3645, 28672, 140625, 513216, 1529437, 3932160, 9034497, 19000000, 37202781, 68677632, 120670225, 203297472, 330328125, 520093696, 796539777, 1190427840, 1740697597, 2496000000, 3516410961, 4875335872, 6661615005, 8981839872
Offset: 1

Views

Author

R. H. Hardin, Mar 10 2012

Keywords

Comments

Row 3 of A209593.

Examples

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

Links

Crossrefs

Cf. A209593.

Programs

  • PARI
    a(n) = (2*n+1)*(n+1)^6; \\ Altug Alkan, Jul 11 2018

Formula

a(n) = (n+1) ^ 6 * (2*n+1).
From Colin Barker, Jul 11 2018: (Start)
G.f.: x*(192 + 2109*x + 4888*x^2 + 2557*x^3 + 352*x^4 - 25*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
(End)

A209595 Number of 4X4 0..n arrays with every element equal to a diagonal or antidiagonal reflection.

Original entry on oeis.org

9216, 1476225, 51380224, 791015625, 7316407296, 47738317081, 241591910400, 1007680691889, 3610000000000, 11438404249041, 32754285674496, 86161557405625, 210866643477504, 484962978515625, 1056630674292736
Offset: 1

Views

Author

R. H. Hardin Mar 10 2012

Keywords

Comments

Row 4 of A209593

Examples

			Some solutions for n=3
..0..0..2..3....0..0..2..0....0..0..2..2....0..0..0..0....0..0..3..3
..0..2..1..2....0..2..2..2....0..2..3..2....0..0..3..0....0..1..2..3
..2..0..0..0....3..2..0..0....0..3..1..0....2..2..3..0....1..3..2..0
..0..2..0..0....3..3..0..0....3..0..0..0....0..2..0..0....2..1..0..0

Links

Formula

a(n) = (n+1) ^ 8 * ((n+1)*(2*n+1)) ^ 2
Showing 1-10 of 13 results. Next

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