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.

A297506 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 31, 29, 1, 12, 68, 110, 87, 1, 21, 218, 314, 531, 280, 1, 37, 729, 1829, 2281, 2534, 876, 1, 65, 2097, 8803, 23348, 14201, 11405, 2735, 1, 114, 6139, 34757, 191192, 270845, 88808, 53175, 8583, 1, 200, 18932, 157673, 1247716, 3624914
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2017

Keywords

Comments

Table starts
.1.....2.......4........7.........12...........21.............37
.1....10......31.......68........218..........729...........2097
.1....29.....110......314.......1829.........8803..........34757
.1....87.....531.....2281......23348.......191192........1247716
.1...280....2534....14201.....270845......3624914.......35049871
.1...876...11405....88808....3075264.....66289769......978288822
.1..2735...53175...573119...35919085...1272836591....28914051279
.1..8583..246040..3613793..414559944..23896899569...823340493402
.1.26900.1135117.22999331.4794512057.450529429259.23748019543354

Examples

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

Links

Crossrefs

Column 2 is A295525.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 11]
k=4: [order 18]
k=5: [order 50]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -6*a(n-4) -8*a(n-5)
n=3: [order 10]
n=4: [order 24]
n=5: [order 59]

A297720 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

Original entry on oeis.org

1, 2, 1, 4, 10, 1, 7, 34, 29, 1, 12, 83, 145, 87, 1, 21, 258, 523, 747, 280, 1, 37, 865, 2717, 4212, 4090, 876, 1, 65, 2651, 14462, 36981, 34319, 21116, 2735, 1, 114, 8041, 68919, 336653, 512354, 268630, 110551, 8583, 1, 200, 25114, 332306, 2699832, 8103241
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2018

Keywords

Comments

Table starts
.1.....2.......4.........7..........12............21..............37
.1....10......34........83.........258...........865............2651
.1....29.....145.......523........2717.........14462...........68919
.1....87.....747......4212.......36981........336653.........2699832
.1...280....4090.....34319......512354.......8103241.......107787351
.1...876...21116....268630.....6812856.....183324631......4021047904
.1..2735..110551...2139403....91994155....4238895126....154327332017
.1..8583..582755..17031173..1242370107...98184350818...5920531350715
.1.26900.3055652.135252357.16741579726.2265008802005.226188909640209

Examples

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

Links

Crossrefs

Column 2 is A295525.
Row 1 is A005251(n+2).

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 13]
k=4: [order 42]
k=5: [order 87]
Empirical for row n:
n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
n=2: a(n) = 4*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4) -24*a(n-5) +24*a(n-6)
n=3: [order 18]
n=4: [order 51]

A295040 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

1, 2, 2, 4, 10, 4, 7, 29, 29, 7, 12, 87, 140, 87, 12, 21, 280, 741, 741, 280, 21, 37, 876, 3853, 6686, 3853, 876, 37, 65, 2735, 19956, 59126, 59126, 19956, 2735, 65, 114, 8583, 104096, 528282, 898493, 528282, 104096, 8583, 114, 200, 26900, 541775, 4738235
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Table starts
...1.....2.......4.........7..........12............21..............37
...2....10......29........87.........280...........876............2735
...4....29.....140.......741........3853.........19956..........104096
...7....87.....741......6686.......59126........528282.........4738235
..12...280....3853.....59126......898493......13706771.......209181266
..21...876...19956....528282....13706771.....355281224......9248214732
..37..2735..104096...4738235...209181266....9248214732....411280569141
..65..8583..541775..42321441..3184995895..240292442848..18227207589288
.114.26900.2819027.378112132.48548926944.6243986963713.807975522778623

Examples

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

Links

Crossrefs

Column 1 is A005251(n+2).
Column 2 is A295525.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
k=3: [order 15]
k=4: [order 34]
k=5: [order 91]
Showing 1-3 of 3 results.

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