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 1-4 of 4 results.

A297544 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 35, 7, 1, 1, 38, 93, 88, 14, 1, 1, 105, 197, 275, 461, 31, 1, 1, 381, 905, 1233, 2205, 2050, 69, 1, 1, 1067, 4617, 10234, 12161, 13248, 8057, 155, 1, 1, 2676, 17190, 65363, 205888, 94647, 67215, 35640, 354, 1, 1, 7533, 60751, 355573
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2017

Keywords

Comments

Table starts
.1...1......1.......1........1...........1.............1..............1
.1...2.....11......24.......38.........105...........381...........1067
.1...4.....35......93......197.........905..........4617..........17190
.1...7.....88.....275.....1233.......10234.........65363.........355573
.1..14....461....2205....12161......205888.......2748026.......25141813
.1..31...2050...13248....94647.....3015179......67372651......916902295
.1..69...8057...67215...754342....45293985....1610981344....33425081735
.1.155..35640..401415..6315609...726450667...45496070039..1479214192234
.1.354.158090.2403621.51451261.11267743659.1204223924807.59920115456355

Examples

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

Links

Crossrefs

Column 2 is A202973.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5)
k=3: [order 14]
k=4: [order 22]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6)
n=3: [order 17]
n=4: [order 40]

A297762 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 12, 4, 1, 1, 31, 52, 7, 1, 1, 78, 206, 186, 14, 1, 1, 225, 734, 1181, 1045, 31, 1, 1, 733, 4088, 7081, 10639, 5685, 69, 1, 1, 2305, 24801, 73352, 109228, 90727, 28565, 155, 1, 1, 7156, 130159, 759243, 2263784, 1456855, 720785, 148681, 354, 1, 1
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2018

Keywords

Comments

Table starts
.1...1......1........1..........1.............1...............1
.1...2.....12.......31.........78...........225.............733
.1...4.....52......206........734..........4088...........24801
.1...7....186.....1181.......7081.........73352..........759243
.1..14...1045....10639.....109228.......2263784........45618455
.1..31...5685....90727....1456855......59707529......2301783905
.1..69..28565...720785...18733087....1504842706....108229776807
.1.155.148681..5909241..251641086...39769163381...5394743533114
.1.354.783104.48847911.3354939709.1043883771677.267870723932943

Examples

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

Links

Crossrefs

Column 2 is A202973.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5)
k=3: [order 15]
k=4: [order 33]
k=5: [order 78]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)
n=3: [order 20]
n=4: [order 52]

A297802 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567
Offset: 1

Views

Author

R. H. Hardin, Jan 06 2018

Keywords

Comments

Table starts
.1...1......1.......1.........1...........1.............1...............1
.1...2.....11......24........38.........105...........381............1067
.1...4.....37.....100.......293........1320..........6215...........24879
.1...7....108.....422......2195.......16006........115773..........738989
.1..14....533....2936.....23781......320168.......4340367........46828204
.1..31...2434...17899....231921.....5511367.....123361724......2122878239
.1..69..10287..104985...2174696....91376524....3420197908.....94927605755
.1.155..45968..645568..21427001..1587468720..102189481612...4611250894511
.1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943

Examples

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

Links

Crossrefs

Column 2 is A202973.
Row 2 is A297545.

Formula

Empirical for column k:
k=1: a(n) = a(n-1),
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5),
k=3: [order 15],
k=4: [order 37],
k=5: [order 95].
Empirical for row n:
n=1: a(n) = a(n-1),
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),
n=3: [order 21],
n=4: [order 55].

A295213 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 10, 7, 1, 1, 14, 27, 27, 14, 1, 1, 31, 102, 147, 102, 31, 1, 1, 69, 345, 916, 916, 345, 69, 1, 1, 155, 1162, 4938, 9536, 4938, 1162, 155, 1, 1, 354, 4072, 27208, 85215, 85215, 27208, 4072, 354, 1, 1, 814, 14224, 152236, 775547, 1245294
Offset: 1

Views

Author

R. H. Hardin, Nov 17 2017

Keywords

Comments

Table starts
.1...1.....1......1........1..........1............1..............1
.1...2.....4......7.......14.........31...........69............155
.1...4....10.....27......102........345.........1162...........4072
.1...7....27....147......916.......4938........27208.........152236
.1..14...102....916.....9536......85215.......775547........7213161
.1..31...345...4938....85215....1245294.....18444470......278238087
.1..69..1162..27208...775547...18444470....444447937....10896495280
.1.155..4072.152236..7213161..278238087..10896495280...436106162865
.1.354.14224.848992.66719868.4170628296.265837272259.17352456088907

Examples

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

Links

Crossrefs

Column 2 is A202973.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5)
k=3: [order 12]
k=4: [order 28]
k=5: [order 78]
Showing 1-4 of 4 results.

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

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