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.

A251143 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

27, 49, 87, 161, 299, 565, 1075, 2065, 3991, 7761, 15163, 29749, 58563, 115617, 228791, 453633, 900875, 1791413, 3566099, 7105137, 14166487, 28262129, 56409627, 112633781, 224967459, 449449345, 898113015, 1794954785, 3587852651
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 2 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5).
Empirical g.f.: x*(27 - 32*x - 60*x^2 + 35*x^3 + 34*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251144 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

53, 87, 143, 247, 433, 777, 1413, 2607, 4863, 9167, 17433, 33417, 64493, 125207, 244303, 478727, 941473, 1857097, 3672373, 7277087, 14444703, 28712287, 57137993, 113812297, 226874333, 452534727, 903105263, 1803032407, 3600922513
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5)..
Empirical g.f.: x*(53 - 72*x - 118*x^2 + 83*x^3 + 74*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251145 Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

107, 161, 247, 401, 667, 1141, 1987, 3521, 6327, 11521, 21227, 39541, 74387, 141201, 270167, 520561, 1009147, 1966581, 3849507, 7563681, 14908407, 29462561, 58351947, 115776501, 230052467, 457677041, 911425687, 1816495121, 3622705627
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5).
Empirical g.f.: x*(107 - 160*x - 236*x^2 + 195*x^3 + 162*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251146 Number of (n+1) X (5+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

213, 299, 433, 667, 1061, 1743, 2925, 5003, 8689, 15307, 27317, 49359, 90237, 166811, 311569, 587515, 1117445, 2141775, 4132941, 8022251, 15650353, 30663019, 60294293, 118919247, 235137501, 465904763, 924738385, 1838035483, 3657558629
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5).
Empirical g.f.: x*(213 - 340*x - 464*x^2 + 433*x^3 + 342*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251147 Number of (n+1) X (6+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

427, 565, 777, 1141, 1743, 2763, 4491, 7453, 12569, 21501, 37255, 65355, 116035, 208469, 378889, 696357, 1293471, 2426507, 4593563, 8767469, 16856057, 32613805, 63450647, 124026251, 243400723, 479274853, 946371561, 1873038613, 3714194799
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 6 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5).
Empirical g.f.: x*(427 - 716*x - 918*x^2 + 945*x^3 + 718*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251148 Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

853, 1075, 1413, 1987, 2925, 4491, 7101, 11491, 18917, 31587, 53389, 91275, 157789, 275843, 487717, 872259, 1577901, 2886539, 5337725, 9971363, 18803813, 35765155, 68549453, 132276107, 256749085, 500872771, 981317541, 1929582211, 3805684077
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Examples

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

Links

Crossrefs

Column 7 of A251149.

Formula

Empirical: a(n) = 3*a(n-1) - 5*a(n-3) + a(n-4) + 2*a(n-5).
Empirical g.f.: x*(853 - 1484*x - 1812*x^2 + 2013*x^3 + 1486*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 26 2018

A251142 Number of (n+1) X (n+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.

Original entry on oeis.org

13, 49, 143, 401, 1061, 2763, 7101, 18193, 46575, 119441, 307045, 791499, 2045725
Offset: 1

Views

Author

R. H. Hardin, Nov 30 2014

Keywords

Comments

Diagonal of A251149.

Examples

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

Crossrefs

Cf. A251149.
Showing 1-7 of 7 results.

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

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