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 1-3 of 3 results.

A302877 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 17, 10, 16, 13, 31, 35, 37, 21, 32, 21, 113, 72, 95, 82, 42, 64, 34, 363, 241, 306, 285, 209, 86, 128, 55, 813, 722, 1442, 1197, 858, 536, 179, 256, 89, 1751, 1821, 5871, 7580, 4849, 2938, 1549, 370, 512, 144, 5001, 4863, 21832, 41498
Offset: 1

Views

Author

R. H. Hardin, Apr 15 2018

Keywords

Comments

Table starts
...1...2....3.....5......8.......13........21..........34...........55
...2...3...11....21.....31......113.......363.........813.........1751
...4...6...17....35.....72......241.......722........1821.........4863
...8..10...37....95....306.....1442......5871.......21832........89400
..16..21...82...285...1197.....7580.....41498......224087......1300510
..32..42..209...858...4849....45897....359518.....2795440.....24612087
..64..86..536..2938..23037...320405...3780984....44148194....588417750
.128.179.1549.11126.114810..2489823..44888558...786125894..15974455418
.256.370.4513.44216.603229.20679119.569313013.14827387374.460770487307

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 56] for n>59
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 60] for n>64

A303040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 14, 10, 16, 13, 31, 28, 35, 21, 32, 21, 113, 56, 74, 71, 42, 64, 34, 363, 150, 234, 197, 186, 86, 128, 55, 813, 360, 869, 703, 544, 459, 179, 256, 89, 1751, 828, 2926, 3069, 2494, 1686, 1287, 370, 512, 144, 5001, 1906, 8500, 11079
Offset: 1

Views

Author

R. H. Hardin, Apr 17 2018

Keywords

Comments

Table starts
...1...2....3.....5......8......13.......21........34.........55..........89
...2...3...11....21.....31.....113......363.......813.......1751........5001
...4...6...14....28.....56.....150......360.......828.......1906........4628
...8..10...35....74....234.....869.....2926......8500......27931.......96592
..16..21...71...197....703....3069....11079.....39281.....147655......574771
..32..42..186...544...2494...13597....59654....251705....1186522.....5869222
..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475
.128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879
.256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 70]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 11] for n>12
n=4: [order 61] for n>62

A303525 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 18, 10, 16, 13, 31, 37, 39, 21, 32, 21, 113, 80, 103, 95, 42, 64, 34, 363, 286, 359, 340, 246, 86, 128, 55, 813, 916, 1875, 1758, 1115, 687, 179, 256, 89, 1751, 2532, 8676, 13031, 9225, 4112, 2023, 370, 512, 144, 5001, 7477, 36072
Offset: 1

Views

Author

R. H. Hardin, Apr 25 2018

Keywords

Comments

Table starts
...1...2....3.....5.......8........13.........21...........34............55
...2...3...11....21......31.......113........363..........813..........1751
...4...6...18....37......80.......286........916.........2532..........7477
...8..10...39...103.....359......1875.......8676........36072........166784
..16..21...95...340....1758.....13031......87730.......569770.......4036330
..32..42..246..1115....9225....102779....1052163.....10663440.....122173279
..64..86..687..4112...56046....965150...15768709....258412452....4730074082
.128.179.2023.16640..366415...9961980..260078546...6835357512..199276300520
.256.370.6126.71025.2519399.109395622.4544413190.190464446456.8858057538977

Examples

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

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302310.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 12] for n>15
k=4: [order 47] for n>49
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 20] for n>21
n=4: [order 58] for n>60
Showing 1-3 of 3 results.

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