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.

A208084 Number of (n+1) X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Original entry on oeis.org

8, 20, 134, 156, 2664, 1224, 54504, 9612, 1119906, 75492, 23025384, 592920, 473447592, 4656852, 9735152022, 36575388, 200177107272, 287266824, 4116102713928, 2256222924, 84636562515282, 17720604900, 1740322886860296
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Comments

Diagonal of A208085.

Examples

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

Links

Crossrefs

Cf. A208085.

A208086 Number of 4 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Original entry on oeis.org

24, 56, 134, 344, 888, 2318, 6056, 15848, 41478, 108584, 284264, 744206, 1948344, 5100824, 13354118, 34961528, 91530456, 239629838, 627359048, 1642447304, 4299982854, 11257501256, 29472520904, 77160061454, 202007663448
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Comments

Row 3 of A208085.

Examples

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

Links

Crossrefs

Cf. A208085.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 2*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = 2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))) / 5.
(End)

A208087 Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Original entry on oeis.org

72, 168, 402, 1032, 2664, 6954, 18168, 47544, 124434, 325752, 852792, 2232618, 5845032, 15302472, 40062354, 104884584, 274591368, 718889514, 1882077144, 4927341912, 12899948562, 33772503768, 88417562712, 231480184362
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Comments

Row 5 of A208085.

Examples

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

Links

Crossrefs

Cf. A208085.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 6*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = (3/5)*2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))).
(End)

A208088 Number of 7 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Original entry on oeis.org

108, 180, 288, 468, 756, 1224, 1980, 3204, 5184, 8388, 13572, 21960, 35532, 57492, 93024, 150516, 243540, 394056, 637596, 1031652, 1669248, 2700900, 4370148, 7071048, 11441196, 18512244, 29953440, 48465684, 78419124, 126884808
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Comments

Row 6 of A208085.

Examples

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

Links

Crossrefs

Cf. A208085.

Formula

Empirical: a(n) = a(n-1) + a(n-2).
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 36*x*(3 + 2*x) / (1 - x - x^2).
a(n) = (9*2^(2-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
(End)

A208089 Number of 8 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.

Original entry on oeis.org

216, 504, 1206, 3096, 7992, 20862, 54504, 142632, 373302, 977256, 2558376, 6697854, 17535096, 45907416, 120187062, 314653752, 823774104, 2156668542, 5646231432, 14782025736, 38699845686, 101317511304, 265252688136, 694440553086
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Comments

Row 7 of A208085.

Examples

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

Links

Crossrefs

Cf. A208085.

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 28 2018: (Start)
G.f.: 18*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = (9/5)*2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))).
(End)
Showing 1-5 of 5 results.

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