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 1-7 of 7 results.

A205187 Number of (n+1)X2 0..1 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

16, 24, 48, 72, 144, 216, 432, 648, 1296, 1944, 3888, 5832, 11664, 17496, 34992, 52488, 104976, 157464, 314928, 472392, 944784, 1417176, 2834352, 4251528, 8503056, 12754584, 25509168, 38263752, 76527504, 114791256, 229582512, 344373768
Offset: 1

Views

Author

R. H. Hardin Jan 23 2012

Keywords

Comments

Column 1 of A205193

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-2)

A205188 Number of (n+1) X 4 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

48, 64, 124, 160, 292, 384, 708, 928, 1708, 2240, 4124, 5408, 9956, 13056, 24036, 31520, 58028, 76096, 140092, 183712, 338212, 443520, 816516, 1070752, 1971244, 2585024, 4759004, 6240800, 11489252, 15066624, 27737508, 36374048, 66964268
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Column 3 of A205193.

Examples

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

Links

Crossrefs

Cf. A205193.

Formula

Empirical: a(n) = 2*a(n-2) +a(n-4) for n>5.
Empirical g.f.: 4*x*(12 + 16*x + 7*x^2 + 8*x^3 - x^4) / (1 - 2*x^2 - x^4). - Colin Barker, Jun 11 2018

A205189 Number of (n+1) X 5 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

72, 104, 160, 256, 384, 576, 864, 1312, 1984, 3008, 4544, 6880, 10400, 15744, 23808, 36032, 54496, 82464, 124736, 188736, 285504, 431968, 653472, 988672, 1495680, 2262848, 3423328, 5179168, 7835328, 11854016, 17933504, 27131360, 41046176
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Column 4 of A205193.

Examples

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

Links

Crossrefs

Cf. A205193.

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) for n>6.
Empirical g.f.: 8*x*(9 + 4*x - 2*x^2 + 8*x^3 - x^5) / (1 - x - x^2 + x^3 - x^4). - Colin Barker, Jun 11 2018

A205190 Number of (n+1) X 6 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

144, 168, 292, 384, 736, 896, 1568, 1920, 3392, 4224, 7520, 9344, 16608, 20608, 36608, 45440, 80736, 100224, 178080, 221056, 392768, 487552, 866272, 1075328, 1910624, 2371712, 4214016, 5230976, 9294304, 11537280, 20499232, 25446272, 45212480
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Column 5 of A205193.

Examples

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

Links

Crossrefs

Cf. A205193.

Formula

Empirical: a(n) = 2*a(n-2) +a(n-6) for n>9.
Empirical g.f.: 4*x*(36 + 42*x + x^2 + 12*x^3 + 38*x^4 + 32*x^5 - 12*x^6 - 10*x^7 - 9*x^8) / (1 - 2*x^2 - x^6). - Colin Barker, Jun 11 2018

A205191 Number of (n+1) X 7 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

216, 272, 384, 576, 896, 1408, 2048, 2944, 4224, 6144, 8960, 13184, 19328, 28416, 41600, 61056, 89344, 131072, 191872, 281472, 412160, 604544, 885376, 1298432, 1901824, 2788736, 4085120, 5989632, 8774784, 12864640, 18848000, 27631104
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Column 6 of A205193.

Examples

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

Links

Crossrefs

Cf. A205193.

Formula

Empirical: a(n) = a(n-1) +a(n-2) -a(n-3) +a(n-4) -a(n-5) +a(n-6) for n>10.
Empirical g.f.: 8*x*(27 + 7*x - 13*x^2 + 17*x^3 - x^4 + 33*x^5 - x^6 - 10*x^7 - 8*x^8 - 8*x^9) / ((1 - x^2 + x^3)*(1 - x - x^3)). - Colin Barker, Jun 11 2018

A205192 Number of (n+1) X 8 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

432, 440, 708, 864, 1568, 2048, 3904, 4608, 7872, 9216, 15808, 18944, 32960, 39936, 69824, 84480, 147520, 178176, 310848, 375296, 654656, 790528, 1379136, 1665536, 2905792, 3509248, 6122432, 7393792, 12899520, 15578112, 27178176, 32821760
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Column 7 of A205193.

Examples

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

Links

Crossrefs

Cf. A205193.

Formula

Empirical: a(n) = 2*a(n-2) +a(n-8) for n>13.
Empirical g.f.: 4*x*(108 + 110*x - 39*x^2 - 4*x^3 + 38*x^4 + 80*x^5 + 192*x^6 + 128*x^7 - 92*x^8 - 110*x^9 - 161*x^10 - 88*x^11 - 56*x^12) / (1 - 2*x^2 - x^8). - Colin Barker, Jun 11 2018

A205186 Number of (n+1) X (n+1) 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.

Original entry on oeis.org

16, 40, 124, 256, 736, 1408, 3904, 7168, 19456, 34816, 93184, 163840, 434176, 753664, 1982464, 3407872, 8912896, 15204352, 39583744, 67108864, 174063616, 293601280, 759169024, 1275068416, 3288334336
Offset: 1

Views

Author

R. H. Hardin, Jan 23 2012

Keywords

Comments

Diagonal of A205193.

Examples

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

Formula

Conjectures from Colin Barker, Jan 17 2018: (Start)
G.f.: 4*x*(4 + 10*x - x^2 - 16*x^3) / ((1 - 2*x)^2*(1 + 2*x)^2).
a(n) = 8*a(n-2) - 16*a(n-4) for n>3.
(End)
Showing 1-7 of 7 results.

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

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