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.

A202973 Number of n X 2 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 2, 4, 7, 14, 31, 69, 155, 354, 814, 1875, 4326, 9993, 23095, 53387, 123430, 285394, 659913, 1525942, 3528541, 8159347, 18867623, 43629460, 100888804, 233295503, 539473228, 1247479743, 2884676711, 6670537293, 15424975984, 35668774074
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Column 2 of A202979.

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) - a(n-5).
Empirical g.f.: x*(1 - x - 3*x^3 - x^4) / (1 - 3*x + 2*x^2 - 2*x^3 + 2*x^4 + x^5). - Colin Barker, Feb 19 2018

A202974 Number of n X 3 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 4, 17, 58, 215, 866, 3507, 14120, 56921, 229860, 928443, 3749720, 15144167, 61165438, 247041429, 997775144, 4029911351, 16276407572, 65738788527, 265512410122, 1072378133103, 4331228325504, 17493399301365, 70654095337584
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Column 3 of A202979.

Examples

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

Crossrefs

Cf. A202979.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 16*a(n-3) - 14*a(n-4) - 3*a(n-5) + 8*a(n-6) - 9*a(n-7) - 2*a(n-8) + 6*a(n-9) + 2*a(n-10).
Empirical g.f.: x*(1 - 2*x + 4*x^2 - 16*x^3 + 4*x^4 + x^5 - 10*x^6 + 4*x^7 + 8*x^8 + 2*x^9) / (1 - 6*x + 11*x^2 - 16*x^3 + 14*x^4 + 3*x^5 - 8*x^6 + 9*x^7 + 2*x^8 - 6*x^9 - 2*x^10). - Colin Barker, Jun 03 2018

A202975 Number of nX4 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 7, 58, 385, 2582, 17740, 122468, 846908, 5858575, 40519184, 280214415, 1937863565, 13401760093, 92683431379, 640976755990, 4432841883249, 30656469034888, 212012773252576, 1466229429328620, 10140090725898534
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 4 of A202979

Examples

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

Formula

Empirical: a(n) = 10*a(n-1) -31*a(n-2) +82*a(n-3) -131*a(n-4) +226*a(n-5) -319*a(n-6) +206*a(n-7) -574*a(n-8) +483*a(n-9) -432*a(n-10) +517*a(n-11) +132*a(n-12) +746*a(n-13) -145*a(n-14) -228*a(n-15) -6*a(n-16) +41*a(n-17) +3*a(n-18) -3*a(n-19)

A202976 Number of nX5 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 14, 215, 2582, 31380, 379788, 4590696, 55723864, 676981428, 8220515870, 99804610105, 1211737645986, 14712070032443, 178624535138225, 2168744883228649, 26331490124843751, 319699729136522144
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 5 of A202979

Examples

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

Formula

Empirical: a(n) = 21*a(n-1) -168*a(n-2) +988*a(n-3) -4019*a(n-4) +14018*a(n-5) -38338*a(n-6) +76250*a(n-7) -75318*a(n-8) -25048*a(n-9) -2704*a(n-10) +284955*a(n-11) -215394*a(n-12) -880505*a(n-13) -242350*a(n-14) +5521214*a(n-15) +653795*a(n-16) -10478457*a(n-17) -9279936*a(n-18) +15930956*a(n-19) +21911876*a(n-20) -8411513*a(n-21) -37124626*a(n-22) -3849041*a(n-23) +23286499*a(n-24) -8400505*a(n-25) -9905859*a(n-26) +47524429*a(n-27) +20129245*a(n-28) -116149038*a(n-29) +2411219*a(n-30) +172063757*a(n-31) -3388918*a(n-32) -136545864*a(n-33) -28219012*a(n-34) +67852922*a(n-35) +54667307*a(n-36) +2102952*a(n-37) -12764701*a(n-38) -5492419*a(n-39) -787424*a(n-40) +318583*a(n-41) +347059*a(n-42) +193761*a(n-43) +39772*a(n-44) -696*a(n-45) -1216*a(n-46)

A202977 Number of nX6 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 31, 866, 17740, 379788, 8071997, 170937904, 3635245483, 77355342983, 1645059084851, 34980781489450, 743874666203318, 15818866015610506, 336395670890580933, 7153607521601342149, 152124673570902721461
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Column 6 of A202979

Examples

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

A202978 Number of n X 7 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 69, 3507, 122468, 4590696, 170937904, 6330398606, 235362503738, 8754859878268, 325475861455984, 12099539397621289, 449821095241853452, 16722911203146960563, 621702975576594657954, 23112884157721171287549
Offset: 1

Views

Author

R. H. Hardin, Dec 26 2011

Keywords

Comments

Column 7 of A202979.

Examples

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

Crossrefs

Cf. A202979.

A202972 Number of n X n 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

Original entry on oeis.org

1, 2, 17, 385, 31380, 8071997, 6330398606, 15305115754880, 113359928263133320, 2565928235760939767164, 177686302889022383527488349, 37653160193950657089306550224687, 24413727008012244865702150476410950284
Offset: 1

Views

Author

R. H. Hardin Dec 26 2011

Keywords

Comments

Diagonal of A202979

Examples

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