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 1-8 of 8 results.

A305047 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 17, 20, 20, 17, 99, 1, 1, 194, 40, 17, 55, 17, 40, 194, 1, 1, 387, 73, 25, 201, 201, 25, 73, 387, 1, 1, 773, 87, 70, 337, 137, 337, 70, 87, 773, 1, 1, 1538, 219, 67, 1359, 42, 42, 1359
Offset: 1

Views

Author

R. H. Hardin, May 24 2018

Keywords

Comments

Table starts
.1...1..1..1....1....1....1.......1.......1.......1.........1..........1
.1...4..7.13...26...49...99.....194.....387.....773......1538.......3081
.1...7..5..9...15...17...40......73......87.....219.......433........583
.1..13..9.11...20...17...25......70......67.....101.......292........325
.1..26.15.20...55..201..337....1359....5918...13840.....50917.....214418
.1..49.17.17..201..137...42....5165....6357....5846....188507.....395242
.1..99.40.25..337...42..116....6542....3137....4862....144931.....173351
.1.194.73.70.1359.5165.6542..273937.1450263.3623207..71239378..487361093
.1.387.87.67.5918.6357.3137.1450263.2062731.1912261.381186998.1094057409

Examples

			Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..1
..1..1..0..0. .1..1..1..1. .1..1..0..1. .0..1..1..0. .0..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..0. .0..0..0..1
..0..1..0..0. .1..1..1..1. .1..1..0..0. .0..1..1..0. .0..0..0..1
..1..0..1..1. .1..1..1..1. .1..1..0..1. .0..1..1..0. .0..0..0..1

Links

Crossrefs

Column 2 is A304004.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 11] for n>13
k=4: [order 9] for n>13

A304141 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 16, 20, 20, 16, 99, 1, 1, 194, 33, 17, 39, 17, 33, 194, 1, 1, 387, 57, 25, 83, 83, 25, 57, 387, 1, 1, 773, 62, 62, 135, 39, 135, 62, 62, 773, 1, 1, 1538, 133, 59, 356, 34, 34, 356, 59, 133
Offset: 1

Views

Author

R. H. Hardin, May 07 2018

Keywords

Comments

Table starts
.1...1..1..1...1...1...1.....1.....1.....1......1.......1.......1........1
.1...4..7.13..26..49..99...194...387...773...1538....3081....6147....12298
.1...7..5..9..15..16..33....57....62...133....231.....256.....549......953
.1..13..9.11..20..17..25....62....59....93....220.....237.....381......830
.1..26.15.20..39..83.135...356...967..1769...4507...12371...26399....63179
.1..49.16.17..83..39..34...749...257...102...8887....2522.....603...104361
.1..99.33.25.135..34..48...785....96...164...5607.....688....1198....43126
.1.194.57.62.356.749.785.11067.31406.35953.290885.1165507.1782306..8735753
.1.387.62.59.967.257..96.31406..8405...577.975952..406351...56557.28610665

Examples

			Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1
..1..0..1..1. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
..1..1..1..1. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
..1..0..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..1..1
..0..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..1

Links

Crossrefs

Column 2 is A304004.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 8] for n>10
k=4: a(n) = 2*a(n-1) +2*a(n-3) -6*a(n-4) +3*a(n-6) for n>10
k=5: [order 91] for n>96

A304676 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 23, 23, 26, 1, 1, 49, 45, 56, 45, 49, 1, 1, 99, 131, 199, 199, 131, 99, 1, 1, 194, 337, 598, 897, 598, 337, 194, 1, 1, 387, 883, 1950, 3525, 3525, 1950, 883, 387, 1, 1, 773, 2389, 6588, 15544, 20932, 15544, 6588, 2389
Offset: 1

Views

Author

R. H. Hardin, May 16 2018

Keywords

Comments

Table starts
.1...1....1.....1......1.......1........1.........1...........1............1
.1...4....7....13.....26......49.......99.......194.........387..........773
.1...7...13....23.....45.....131......337.......883........2389.........6599
.1..13...23....56....199.....598.....1950......6588.......21871........72947
.1..26...45...199....897....3525....15544.....68896......310438......1387613
.1..49..131...598...3525...20932...122388....711362.....4369285.....26155072
.1..99..337..1950..15544..122388...930123...7208807....57718628....454436233
.1.194..883..6588..68896..711362..7208807..73484449...779364745...8098139458
.1.387.2389.21871.310438.4369285.57718628.779364745.11082127004.153249721883

Examples

			Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..0
..1..1..0..1. .0..0..0..0. .0..0..0..0. .0..1..0..1. .1..1..0..1
..0..1..0..1. .0..0..0..0. .1..1..1..1. .0..0..0..1. .0..1..0..1
..0..0..1..1. .0..0..0..0. .1..1..1..1. .1..1..0..1. .0..0..1..1
..1..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..0. .1..1..1..0

Links

Crossrefs

Column 2 is A304004.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 18] for n>19
k=4: [order 70] for n>71

A304952 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 29, 26, 29, 49, 1, 1, 99, 58, 70, 70, 58, 99, 1, 1, 194, 120, 139, 189, 139, 120, 194, 1, 1, 387, 250, 287, 468, 468, 287, 250, 387, 1, 1, 773, 515, 625, 1436, 1916, 1436, 625, 515, 773, 1, 1, 1538
Offset: 1

Views

Author

R. H. Hardin, May 22 2018

Keywords

Comments

Table starts
.1...1...1....1.....1.....1......1.......1........1........1.........1
.1...4...7...13....26....49.....99.....194......387......773......1538
.1...7..13...21....29....58....120.....250......515.....1100......2302
.1..13..21...26....70...139....287.....625.....1484.....3197......7321
.1..26..29...70...189...468...1436....3753....11101....32272.....92418
.1..49..58..139...468..1916...5296...17450....62128...207139....693887
.1..99.120..287..1436..5296..18950...76117...313593..1223755...4910872
.1.194.250..625..3753.17450..76117..401301..2043622..9772099..49480464
.1.387.515.1484.11101.62128.313593.2043622.12197817.69375211.421959328

Examples

			Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..1..0
..1..0..0..1. .1..1..0..1. .0..0..0..1. .1..0..1..1. .1..1..0..1
..0..1..1..0. .1..0..1..0. .1..1..1..1. .1..1..1..0. .1..1..1..0
..1..0..0..1. .0..0..1..0. .1..0..0..0. .0..0..1..1. .1..1..0..1
..0..1..1..0. .1..1..0..1. .1..0..0..0. .1..0..0..0. .0..0..1..0

Links

Crossrefs

Column 2 is A304004.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 18] for n>19
k=4: [order 70] for n>71

A316123 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 23, 23, 26, 1, 1, 49, 47, 56, 47, 49, 1, 1, 99, 144, 213, 213, 144, 99, 1, 1, 194, 391, 702, 1109, 702, 391, 194, 1, 1, 387, 1118, 2524, 5426, 5426, 2524, 1118, 387, 1, 1, 773, 3330, 9034, 26626, 43480, 26626, 9034
Offset: 1

Views

Author

R. H. Hardin, Jun 24 2018

Keywords

Comments

Table starts
.1...1....1.....1......1........1.........1..........1............1
.1...4....7....13.....26.......49........99........194..........387
.1...7...13....23.....47......144.......391.......1118.........3330
.1..13...23....56....213......702......2524.......9034........33185
.1..26...47...213...1109.....5426.....26626.....133245.......708063
.1..49..144...702...5426....43480....283238....2064800.....15977233
.1..99..391..2524..26626...283238...2525039...25192165....261795432
.1.194.1118..9034.133245..2064800..25192165..351431316...5223691497
.1.387.3330.33185.708063.15977233.261795432.5223691497.112149224917

Examples

			Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..0..0
..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1. .1..1..1..1
..1..0..1..1. .1..1..1..0. .0..1..1..0. .1..0..0..1. .1..1..1..1
..0..1..0..1. .0..0..1..1. .1..1..0..1. .1..1..1..0. .1..1..1..1
..1..0..0..1. .1..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0

Links

Crossrefs

Column 2 is A304004.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 17] for n>19
k=4: [order 70] for n>71

A305360 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 27, 26, 27, 49, 1, 1, 99, 53, 64, 64, 53, 99, 1, 1, 194, 99, 115, 137, 115, 99, 194, 1, 1, 387, 197, 211, 271, 271, 211, 197, 387, 1, 1, 773, 371, 439, 656, 538, 656, 439, 371, 773, 1, 1, 1538, 713, 870
Offset: 1

Views

Author

R. H. Hardin, May 31 2018

Keywords

Comments

Table starts
.1...1...1...1....1....1.....1.....1......1.......1.......1........1........1
.1...4...7..13...26...49....99...194....387.....773....1538.....3081.....6147
.1...7..13..21...27...53....99...197....371.....713....1365.....2645.....5105
.1..13..21..26...64..115...211...439....870....1725....3513.....7141....14372
.1..26..27..64..137..271...656..1414...3251....7823...17334....40796....93604
.1..49..53.115..271..538..1476..3001...8018...19631...49142...121150...301994
.1..99..99.211..656.1476..4429.11281..31062...84750..233266...652271..1795948
.1.194.197.439.1414.3001.11281.33136..96562..302341..927289..2823816..8720038
.1.387.371.870.3251.8018.31062.96562.321576.1100993.3656995.12269156.41412932

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..0..1..1. .0..0..0..0
..0..0..1..1. .1..0..1..0. .1..0..1..1. .1..1..0..0. .1..1..1..1
..1..1..1..1. .1..0..0..1. .0..1..0..1. .1..1..1..0. .1..0..0..1
..1..1..0..0. .1..0..1..0. .0..1..0..0. .0..0..1..0. .0..0..1..0
..1..1..0..0. .0..1..1..0. .1..0..1..1. .1..0..0..1. .1..1..1..0

Links

Crossrefs

Column 2 is A304004.
Column 3 is A304005.
Column 4 is A304006.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 16] for n>17
k=4: [order 67] for n>70

A316620 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 29, 26, 29, 49, 1, 1, 99, 58, 70, 70, 58, 99, 1, 1, 194, 120, 139, 189, 139, 120, 194, 1, 1, 387, 250, 287, 468, 468, 287, 250, 387, 1, 1, 773, 515, 625, 1446, 1916, 1446, 625, 515, 773, 1, 1, 1538
Offset: 1

Views

Author

R. H. Hardin, Jul 08 2018

Keywords

Comments

Table starts
.1...1...1....1.....1.....1......1.......1........1.........1.........1
.1...4...7...13....26....49.....99.....194......387.......773......1538
.1...7..13...21....29....58....120.....250......515......1100......2302
.1..13..21...26....70...139....287.....625.....1484......3197......7321
.1..26..29...70...189...468...1446....3769....11196.....32714.....93764
.1..49..58..139...468..1916...5428...18126....66146....225773....773853
.1..99.120..287..1446..5428..20777...86855...376999...1555947...6605299
.1.194.250..625..3769.18126..86855..476965..2572180..13348093..71288692
.1.387.515.1484.11196.66146.376999.2572180.16700783.105494740.692447139

Examples

			Some solutions for n=5 k=4
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..1..0
..1..1..0..0. .1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1
..1..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..1..1. .1..0..0..1
..1..0..1..1. .1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..0..1
..0..1..1..0. .1..0..0..1. .0..1..1..0. .0..1..0..0. .0..1..1..0

Links

Crossrefs

Column 2 is A304004.
Column 3 is A304947.
Column 4 is A304948.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 18] for n>19
k=4: [order 70] for n>71

A316733 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 17, 20, 20, 17, 99, 1, 1, 194, 40, 17, 55, 17, 40, 194, 1, 1, 387, 73, 25, 201, 201, 25, 73, 387, 1, 1, 773, 87, 70, 337, 137, 337, 70, 87, 773, 1, 1, 1538, 219, 67, 1359, 42, 42, 1359
Offset: 1

Views

Author

R. H. Hardin, Jul 11 2018

Keywords

Comments

Starts to differ from A305047 at (n=7, k=7). - R. H. Hardin, Aug 04 2018
Table starts
.1...1..1..1....1....1....1.......1.......1.......1.........1..........1
.1...4..7.13...26...49...99.....194.....387.....773......1538.......3081
.1...7..5..9...15...17...40......73......87.....219.......433........583
.1..13..9.11...20...17...25......70......67.....101.......292........325
.1..26.15.20...55..201..337....1359....5918...13840.....50917.....214418
.1..49.17.17..201..137...42....5165....6357....5846....188507.....395242
.1..99.40.25..337...42..275....6652....3399....8908....160954.....203593
.1.194.73.70.1359.5165.6652..274113.1476693.3813273..72793968..506693539
.1.387.87.67.5918.6357.3399.1476693.2083319.2387357.399292140.1133955731

Examples

			Some solutions for n=5 k=4
..0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..0..0..0..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..0..0..0..0. .1..0..1..1. .1..1..1..1. .1..1..1..1. .0..0..0..0
..0..0..0..0. .0..1..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1

Links

Crossrefs

Column 2 is A304004.
Column 3 is A305042.
Column 4 is A305043.
Column 5 is A305044.
Column 6 is A305045.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
k=3: [order 11] for n>13
k=4: [order 9] for n>13
Showing 1-8 of 8 results.

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

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