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 1-6 of 6 results.

A317759 Number of nX2 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

2, 6, 10, 20, 42, 89, 190, 407, 873, 1874, 4024, 8642, 18561, 39866, 85627, 183917, 395034, 848492, 1822474, 3914489, 8407926, 18059375, 38789713, 83316386, 178955184, 384377666, 825604417, 1773314930, 3808901427, 8181135701
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Column 2 of A317764.

Examples

			Some solutions for n=5
..0..0. .0..1. .0..1. .0..0. .0..0. .0..0. .0..0. .0..0. .0..1. .0..0
..1..1. .1..1. .1..1. .1..1. .1..1. .0..0. .0..1. .0..1. .1..1. .0..0
..1..1. .0..0. .1..1. .1..0. .1..1. .0..0. .1..1. .1..1. .0..0. .1..1
..0..0. .0..0. .1..1. .0..0. .1..1. .0..1. .0..0. .1..1. .0..1. .1..1
..0..0. .1..1. .1..0. .0..1. .0..0. .1..1. .0..1. .1..0. .1..1. .0..0

Links

Crossrefs

Cf. A317764.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6

A317760 Number of nX4 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 20, 28, 43, 72, 127, 232, 432, 813, 1539, 2922, 5557, 10577, 20141, 38362, 73076, 139212, 265212, 505263, 962600, 1833903, 3493880, 6656412, 12681561, 24160471, 46029702, 87694221, 167072053, 318300013, 606414406, 1155320200, 2201076948
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Column 4 of A317764.

Examples

			Some solutions for n=5
..0..1..1..0. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..1..1
..1..1..0..0. .0..0..1..1. .0..0..0..1. .0..0..0..0. .1..1..1..1
..1..0..0..1. .0..1..1..0. .0..0..1..1. .0..0..0..0. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..1..1..1. .0..0..0..1. .0..0..0..0
..0..1..1..1. .1..0..0..0. .1..1..1..0. .0..0..1..1. .0..0..0..0

Links

Crossrefs

Cf. A317764.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) +a(n-5) for n>6

A317761 Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 42, 52, 72, 109, 177, 302, 532, 955, 1733, 3164, 5796, 10637, 19541, 35918, 66040, 121443, 223345, 410772, 755504, 1389565, 2555785, 4700798, 8646092, 15902619, 29249453, 53798108, 98950124, 181997629, 334745805, 615693502, 1132436880
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Column 5 of A317764.

Examples

			Some solutions for n=5:
  0 0 0 0 0      0 0 0 0 0      0 0 0 0 0      0 1 1 0 0
  1 1 1 1 1      1 1 1 1 1      0 0 0 0 1      1 1 0 0 0
  1 1 1 1 1      1 1 1 1 1      0 0 0 1 1      1 0 0 0 0
  1 1 1 1 1      1 1 1 1 0      0 0 1 1 1      0 0 0 0 0
  0 0 0 0 0      1 1 1 0 0      0 1 1 1 1      0 0 0 0 1

Links

Crossrefs

Cf. A317764.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-4) for n > 6.

A317762 Number of nX6 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 89, 100, 127, 177, 266, 425, 709, 1217, 2126, 3753, 6666, 11882, 21223, 37952, 67914, 121578, 217696, 389856, 698220, 1250549, 2239862, 4011891, 7185904, 12871122, 23054360, 41294363, 73965487, 132485357, 237305006, 425055936
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Column 6 of A317764.

Examples

			Some solutions for n=5
..0..0..0..0..0..0. .0..1..1..0..0..0. .0..0..1..1..0..0. .0..0..0..0..0..0
..1..1..1..1..1..1. .0..1..1..0..0..0. .0..1..1..0..0..1. .0..0..0..0..0..1
..1..1..1..1..1..1. .0..1..1..0..0..0. .1..1..0..0..1..1. .0..0..0..0..1..1
..1..1..1..1..1..0. .0..1..1..0..0..0. .1..0..0..1..1..0. .0..0..0..1..1..0
..1..1..1..1..0..0. .0..1..1..0..0..1. .0..0..1..1..0..0. .0..0..1..1..0..0

Links

Crossrefs

Cf. A317764.

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) +a(n-7) for n>10

A317763 Number of nX7 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 190, 196, 232, 302, 425, 639, 1012, 1663, 2801, 4792, 8278, 14385, 25088, 43852, 76756, 134466, 235697, 413288, 724863, 1271539, 2230756, 3913889, 6867349, 12050002, 21144516, 37103735, 65109496, 114255232, 200498730, 351843854
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Column 7 of A317764.

Examples

			Some solutions for n=5
..0..1..1..1..1..0..0. .0..0..0..1..0..0..0. .0..0..0..0..1..1..1
..1..1..1..1..0..0..0. .0..0..1..1..0..0..0. .0..0..0..1..1..1..1
..1..1..1..0..0..0..0. .0..1..1..1..0..0..0. .0..0..1..1..1..1..0
..1..1..0..0..0..0..1. .1..1..1..1..0..0..1. .0..1..1..1..1..0..0
..1..0..0..0..0..1..1. .1..1..1..1..0..1..1. .1..1..1..1..0..0..0

Links

Crossrefs

Cf. A317764.

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -a(n-4) +a(n-5) -a(n-6) +a(n-7) for n>11

A317758 Number of nXn 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 6, 16, 43, 109, 266, 639, 1529, 3674, 8909, 21853, 54252, 136213, 345373, 882828, 2271143, 5871373, 15234214, 39633091, 103306417, 269641062, 704462713, 1841692605, 4816973880, 12602801545
Offset: 1

Views

Author

R. H. Hardin, Aug 06 2018

Keywords

Comments

Diagonal of A317764.

Examples

			Some solutions for n=5
..0..1..1..1..1. .0..1..1..1..1. .0..1..1..1..1. .0..0..0..0..0
..1..1..1..1..1. .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..1..1..1..1. .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..1..1. .0..0..0..0..0. .1..1..1..0..0. .0..0..0..0..1

Crossrefs

Cf. A317764.
Showing 1-6 of 6 results.

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