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 1-10 of 16 results. Next

A266101 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors exactly one smaller than itself.

Original entry on oeis.org

1, 3, 1, 4, 5, 1, 5, 13, 16, 1, 9, 36, 64, 39, 1, 16, 100, 161, 230, 105, 1, 25, 233, 736, 929, 1012, 272, 1, 39, 680, 3846, 6307, 4893, 3928, 715, 1, 64, 2201, 16103, 52171, 53442, 26948, 16428, 1869, 1, 105, 6508, 62778, 371130, 841668, 457738, 145274, 65736
Offset: 1

Views

Author

R. H. Hardin, Dec 21 2015

Keywords

Comments

Table starts
.1.....3.......4........5..........9...........16.............25
.1.....5......13.......36........100..........233............680
.1....16......64......161........736.........3846..........16103
.1....39.....230......929.......6307........52171.........371130
.1...105....1012.....4893......53442.......841668........9880139
.1...272....3928....26948.....457738.....12401485......240721036
.1...715...16428...145274....3899732....192212829.....6206090116
.1..1869...65736...790986...33335734...2895851074...154469020054
.1..4896..269908..4286644..284461696..44366390231..3932140956510
.1.12815.1091720.23281595.2429715557.672954998752.98694163378141

Examples

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

Links

Crossrefs

Column 2 is A121646(n+2).
Row 1 is A195971.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
k=3: a(n) = a(n-1) +12*a(n-2) +5*a(n-3) -12*a(n-4) -2*a(n-5)
k=4: [order 15] for n>16
k=5: [order 17] for n>20
k=6: [order 72] for n>75
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3) +a(n-4)
n=2: [order 16] for n>19
n=3: [order 64] for n>68

A266131 T(n,k) = Number of n X k integer arrays with each element equal to the number of horizontal, diagonal and antidiagonal neighbors exactly one smaller than itself.

Original entry on oeis.org

1, 3, 1, 4, 9, 1, 5, 25, 20, 1, 9, 49, 77, 61, 1, 16, 149, 117, 385, 189, 1, 25, 625, 278, 572, 2099, 544, 1, 39, 2141, 1959, 3851, 4336, 9083, 1629, 1, 64, 5433, 11044, 44623, 62104, 19750, 48188, 4973, 1, 105, 17269, 36730, 347576, 1285961, 326145, 102201, 249446
Offset: 1

Views

Author

R. H. Hardin, Dec 21 2015

Keywords

Comments

Table starts
.1.....3.......4........5.........9.........16..........25.........39
.1.....9......25.......49.......149........625........2141.......5433
.1....20......77......117.......278.......1959.......11044......36730
.1....61.....385......572......3851......44623......347576....1650710
.1...189....2099.....4336.....62104....1285961....16386099..124675418
.1...544....9083....19750....326145...13689944...325554385.3901509248
.1..1629...48188...102201...4176690..311260836.10444421518
.1..4973..249446...620508..50677045.6688962679
.1.15040.1166325..3041449.367191341
.1.45739.6288299.16217839

Examples

			Some solutions for n=4, k=4
..0..0..1..1....0..2..1..2....1..0..2..1....2..1..2..0....0..2..1..0
..0..2..0..1....0..0..1..2....0..2..0..1....0..1..2..0....0..2..1..1
..0..0..1..2....0..2..0..2....3..2..1..1....1..0..2..0....0..2..0..2
..0..2..1..2....0..0..1..1....0..2..1..0....1..1..0..0....0..0..1..1

Links

Crossrefs

Column 2 is A196212.
Row 1 is A195971.

Formula

Empirical for column k:
k=1: a(n) = a(n-1),
k=2: [order 10],
k=3: [order 26] for n>27,
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3) +a(n-4),
n=2: [order 17],
n=3: [order 77].

A196218 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,2,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 20, 20, 5, 9, 61, 58, 61, 9, 16, 189, 290, 290, 189, 16, 25, 544, 1217, 2161, 1217, 544, 25, 39, 1629, 5110, 14605, 14605, 5110, 1629, 39, 64, 4973, 21969, 101780, 173216, 101780, 21969, 4973, 64, 105, 15040, 93666, 723029, 1937895
Offset: 1

Views

Author

R. H. Hardin Sep 29 2011

Keywords

Comments

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 4's
Table starts
...1.....3.......4.........5...........9............16..............25
...3.....9......20........61.........189...........544............1629
...4....20......58.......290........1217..........5110...........21969
...5....61.....290......2161.......14605........101780..........723029
...9...189....1217.....14605......173216.......1937895........21716929
..16...544....5110....101780.....1937895......33962624.......608417005
..25..1629...21969....723029....21716929.....608417005.....17831030743
..39..4973...93666...5056631...244152037...11132866106....525537881675
..64.15040..399920..35105556..2771090244..202301552532..15318916228421
.105.45739.1714601.245353935.31410926798.3661731514195.446553011295591

Examples

			Some solutions for n=6 k=4
..0..0..2..1....0..1..1..0....1..0..2..1....0..1..1..0....1..0..0..0
..1..2..1..0....2..1..1..2....1..2..1..0....0..1..1..1....1..0..0..0
..1..0..1..2....1..0..0..1....0..2..1..0....1..2..0..1....1..1..2..1
..1..0..1..1....1..1..2..1....0..1..1..0....2..0..0..1....0..2..2..1
..2..0..2..0....0..2..0..0....0..1..2..0....1..1..1..2....0..1..1..0
..1..0..1..1....1..1..0..0....1..2..0..0....0..2..1..0....0..1..2..0

Links

Crossrefs

Column 1 is A195971

A196300 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 20, 20, 5, 9, 61, 58, 61, 9, 16, 187, 290, 290, 187, 16, 25, 536, 1201, 2161, 1201, 536, 25, 39, 1597, 4988, 14231, 14231, 4988, 1597, 39, 64, 4849, 21344, 97892, 160800, 97892, 21344, 4849, 64, 105, 14582, 90150, 686759, 1752855, 1752855
Offset: 1

Views

Author

R. H. Hardin Sep 30 2011

Keywords

Comments

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 4's, every 4 is next to 4 2's
Table starts
...1.....3.......4.........5...........9............16..............25
...3.....9......20........61.........187...........536............1597
...4....20......58.......290........1201..........4988...........21344
...5....61.....290......2161.......14231.........97892..........686759
...9...187....1201.....14231......160800.......1752855........19123802
..16...536....4988.....97892.....1752855......29726608.......513362648
..25..1597...21344....686759....19123802.....513362648.....14372583192
..39..4849...90150...4731033...207927811....9011375854....402254701097
..64.14582..381754..32374680..2289816421..157499416616..11172616795189
.105.44097.1621695.222897413.25196042496.2741611675889.309961960884860

Examples

			Some solutions for n=6 k=4
..1..1..2..1....1..0..1..1....1..1..1..1....1..0..0..0....0..1..1..0
..0..0..0..0....1..0..2..0....0..0..0..0....1..2..1..1....0..1..2..0
..1..2..1..1....1..0..1..1....0..0..2..1....0..0..2..2....1..1..2..0
..1..0..1..2....2..1..1..1....0..0..1..2....0..0..1..1....1..0..1..2
..2..1..2..0....0..2..0..0....1..2..1..0....0..2..1..0....2..0..2..1
..0..1..2..1....0..1..1..1....1..0..1..1....0..1..2..0....1..0..0..0

Links

Crossrefs

Column 1 is A195971

A197280 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 14, 14, 5, 9, 29, 34, 29, 9, 16, 67, 92, 92, 67, 16, 25, 134, 317, 627, 317, 134, 25, 39, 275, 888, 2731, 2731, 888, 275, 39, 64, 583, 2626, 11850, 16890, 11850, 2626, 583, 64, 105, 1210, 8078, 57137, 114205, 114205, 57137, 8078, 1210, 105, 169
Offset: 1

Views

Author

R. H. Hardin Oct 12 2011

Keywords

Comments

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
Table starts
...1....3.....4.......5.........9..........16...........25.............39
...3....9....14......29........67.........134..........275............583
...4...14....34......92.......317.........888.........2626...........8078
...5...29....92.....627......2731.......11850........57137.........276689
...9...67...317....2731.....16890......114205.......886737........6017949
..16..134...888...11850....114205.....1276986.....13500114......135563958
..25..275..2626...57137....886737....13500114....209785488.....3332948197
..39..583..8078..276689...6017949...135563958...3332948197....84453386767
..64.1210.24103.1344992..40918349..1464662469..55701159000..2019696975436
.105.2511.72107.6445595.290053910.15975572837.888511016495.47417406612765

Examples

			Some solutions containing all values 0 to 4 for n=6 k=4
..2..1..0..1....1..0..1..2....1..0..0..1....1..0..1..1....1..0..1..2
..1..4..1..1....1..1..4..1....3..1..3..1....3..1..1..0....1..1..4..1
..0..1..3..0....0..3..1..0....1..4..1..0....1..4..1..0....0..3..1..0
..0..3..1..0....0..1..1..0....0..1..3..0....0..1..3..1....0..1..3..1
..0..1..1..0....0..3..1..0....0..1..1..0....1..1..0..1....1..1..0..1
..1..2..2..1....0..1..1..0....1..2..2..1....2..1..0..1....2..1..0..1

Links

Crossrefs

Column 1 is A195971

A197409 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,1,1,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 20, 20, 5, 9, 71, 60, 71, 9, 16, 227, 358, 358, 227, 16, 25, 664, 1626, 3305, 1626, 664, 25, 39, 2107, 7232, 25621, 25621, 7232, 2107, 39, 64, 6675, 34717, 199384, 356211, 199384, 34717, 6675, 64, 105, 20696, 160988, 1634731, 4499426
Offset: 1

Views

Author

R. H. Hardin Oct 14 2011

Keywords

Comments

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
Table starts
...1.....3.......4.........5............9.............16...............25
...3.....9......20........71..........227............664.............2107
...4....20......60.......358.........1626...........7232............34717
...5....71.....358......3305........25621.........199384..........1634731
...9...227....1626.....25621.......356211........4499426.........60334353
..16...664....7232....199384......4499426.......93153650.......2065093081
..25..2107...34717...1634731.....60334353.....2065093081......77683473682
..39..6675..160988..13013551....801294395....45796265386....2861267797023
..64.20696..748843.103260478..10631272297..1003308210971..104224692369107
.105.65029.3514426.825286477.141478252511.22026879283832.3821001855576417

Examples

			Some solutions containing all values 0 to 4 for n=6 k=4
..0..1..1..0....2..1..2..0....2..1..1..0....1..0..1..2....2..1..2..0
..0..2..2..1....1..0..1..1....1..0..2..0....1..0..1..1....1..0..1..1
..0..1..3..1....1..0..1..3....1..0..1..1....1..0..2..0....3..1..4..1
..1..4..1..0....1..1..4..1....2..1..4..1....3..1..1..0....1..4..1..0
..1..1..1..2....0..1..1..0....0..1..1..0....1..4..1..0....0..1..1..0
..0..0..0..1....1..3..1..0....1..3..1..0....0..1..2..0....1..3..1..0

Links

Crossrefs

Column 1 is A195971

A197537 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,1,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 16, 16, 5, 9, 33, 56, 33, 9, 16, 73, 216, 216, 73, 16, 25, 160, 868, 1419, 868, 160, 25, 39, 361, 3500, 9373, 9373, 3500, 361, 39, 64, 835, 14085, 62586, 107655, 62586, 14085, 835, 64, 105, 1966, 56842, 423085, 1220630, 1220630, 423085, 56842
Offset: 1

Views

Author

R. H. Hardin Oct 16 2011

Keywords

Comments

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's
Table starts
...1....3......4.........5...........9............16..............25
...3....9.....16........33..........73...........160.............361
...4...16.....56.......216.........868..........3500...........14085
...5...33....216......1419........9373.........62586..........423085
...9...73....868......9373......107655.......1220630........14056707
..16..160...3500.....62586.....1220630......23325250.......454280983
..25..361..14085....423085....14056707.....454280983.....14991391782
..39..835..56842...2879723...162042137....8844380028....493785636151
..64.1966.229706..19671764..1874230689..172982554332..16343961543732
.105.4703.928664.134643523.21698542215.3386294190736.541269402906501

Examples

			Some solutions containing all values 0 to 4 for n=6 k=4
..0..3..0..1....0..3..0..0....0..3..0..0....0..0..0..1....0..3..0..1
..0..0..3..2....0..0..4..0....3..0..4..0....3..0..3..2....3..0..3..2
..0..4..0..1....0..0..0..0....0..4..0..0....0..4..0..1....0..4..0..1
..0..0..3..2....1..3..0..0....3..0..3..0....0..0..3..1....0..0..3..1
..0..0..0..1....1..0..3..0....0..3..2..1....0..4..0..0....0..0..0..0
..0..0..0..1....2..1..2..1....0..0..1..2....0..0..3..0....1..1..1..1

Links

Crossrefs

Column 1 is A195971

A197672 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 22, 22, 5, 9, 71, 95, 71, 9, 16, 217, 546, 546, 217, 16, 25, 642, 2765, 5005, 2765, 642, 25, 39, 1963, 14503, 44323, 44323, 14503, 1963, 39, 64, 5963, 74812, 403960, 709083, 403960, 74812, 5963, 64, 105, 18018, 386556, 3675345, 11277331
Offset: 1

Views

Author

R. H. Hardin Oct 17 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's
Table starts
...1.....3........4..........5............9..............16................25
...3.....9.......22.........71..........217.............642..............1963
...4....22.......95........546.........2765...........14503.............74812
...5....71......546.......5005........44323..........403960...........3675345
...9...217.....2765......44323.......709083........11277331.........178113620
..16...642....14503.....403960.....11277331.......311676959........8613257822
..25..1963....74812....3675345....178113620......8613257822......417293944115
..39..5963...386556...33272751...2824369075....239118653300....20252638815131
..64.18018..2008698..301565202..44803424135...6630227642552...981414876628367
.105.54753.10415923.2734015025.710299706355.183756345226485.47569549221404522

Examples

			Some solutions containing all values 0 to 4 for n=6 k=4
..0..3..0..0....1..1..2..1....0..1..2..0....1..0..0..0....0..2..1..0
..0..0..0..3....0..0..0..0....1..4..1..0....2..0..3..0....0..1..4..1
..0..0..3..0....0..3..0..0....2..1..1..0....1..0..1..2....0..1..1..1
..2..1..2..0....0..2..1..2....0..0..3..0....1..1..4..1....0..3..0..0
..1..4..1..0....0..1..4..1....0..3..0..0....0..1..1..0....0..0..0..0
..0..1..1..0....0..2..1..0....1..1..0..0....0..1..1..0....0..0..3..0

Links

Crossrefs

Column 1 is A195971

A266025 T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal, vertical and antidiagonal neighbors exactly one smaller than itself.

Original entry on oeis.org

1, 3, 3, 4, 7, 4, 5, 14, 14, 5, 9, 42, 33, 42, 9, 16, 99, 91, 91, 99, 16, 25, 259, 316, 577, 316, 259, 25, 39, 719, 1045, 3796, 3796, 1045, 719, 39, 64, 1784, 3394, 19688, 39064, 19688, 3394, 1784, 64, 105, 4792, 11102, 110924, 336357, 336357, 110924, 11102, 4792, 105
Offset: 1

Views

Author

R. H. Hardin, Dec 20 2015

Keywords

Comments

Table starts
...1.....3......4........5..........9...........16...........25............39
...3.....7.....14.......42.........99..........259..........719..........1784
...4....14.....33.......91........316.........1045.........3394.........11102
...5....42.....91......577.......3796........19688.......110924........656555
...9....99....316.....3796......39064.......336357......3254726......31035211
..16...259...1045....19688.....336357......4285397.....63460724.....950319651
..25...719...3394...110924....3254726.....63460724...1577145547...38948760562
..39..1784..11102...656555...31035211....950319651..38948760562.1561479265416
..64..4792..36842..3732300..292685424..13831198142.916245375526
.105.12479.122052.21344656.2799525337.203362718849

Examples

			Some solutions for n=4 k=4
..1..0..0..1....0..1..2..1....0..1..1..0....0..0..1..2....1..0..1..2
..1..2..3..2....1..3..2..0....2..1..1..1....0..2..2..1....1..1..3..1
..1..2..3..1....2..1..2..0....0..1..1..1....1..2..0..2....2..2..2..0
..0..1..2..0....0..2..1..1....2..1..0..1....1..0..0..1....0..1..2..1

Links

Crossrefs

Column 1 is A195971.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-3) +a(n-4)
k=2: [order 21]
k=3: [order 94] for n>95

A196685 T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 3, 4, 9, 4, 5, 20, 20, 5, 9, 61, 58, 61, 9, 16, 189, 292, 292, 189, 16, 25, 544, 1235, 2245, 1235, 544, 25, 39, 1629, 5186, 15395, 15395, 5186, 1629, 39, 64, 4973, 22461, 109528, 188078, 109528, 22461, 4973, 64, 105, 15040, 96256, 796557, 2169685
Offset: 1

Views

Author

R. H. Hardin Oct 05 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 2's, every 4 is next to 4 3's
Table starts
...1.....3.......4.........5...........9............16..............25
...3.....9......20........61.........189...........544............1629
...4....20......58.......292........1235..........5186...........22461
...5....61.....292......2245.......15395........109528..........796557
...9...189....1235.....15395......188078.......2169685........25142624
..16...544....5186....109528.....2169685......39696088.......741925729
..25..1629...22461....796557....25142624.....741925729.....23029545105
..39..4973...96256...5702355...291420839...14189246566....718199634805
..64.15040..413032..40479328..3417608122..269528695666..22138818455076
.105.45739.1780597.289195575.40048090008.5096101360077.682005890331480

Examples

			Some solutions for n=6 k=4
..0..0..1..1....1..1..0..1....0..0..0..1....0..0..0..0....1..0..0..0
..1..1..2..0....0..1..1..1....0..0..0..2....1..1..2..0....1..2..1..1
..2..1..0..0....0..1..1..0....0..0..0..1....2..2..1..0....0..2..1..2
..0..1..2..0....0..1..1..0....1..2..1..2....1..2..2..0....1..1..0..0
..2..1..1..0....0..2..1..0....1..0..2..0....0..1..1..2....1..1..0..0
..1..0..2..1....0..0..2..1....2..1..1..0....1..2..0..1....0..1..2..1

Links

Crossrefs

Column 1 is A195971
Column 2 is A196212
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