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.

A205161 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 2, 4, 15, 4, 12, 159, 159, 12, 40, 2191, 6941, 2191, 40, 143, 31168, 332285, 332285, 31168, 143, 528, 447343, 15821727, 54314298, 15821727, 447343, 528, 1979, 6427791, 754700909, 8797534495, 8797534495, 754700909, 6427791, 1979, 7466, 92387812
Offset: 1

Views

Author

R. H. Hardin Jan 22 2012

Keywords

Comments

Table starts
....1........2.............4................12....................40
....2.......15...........159..............2191.................31168
....4......159..........6941............332285..............15821727
...12.....2191........332285..........54314298............8797534495
...40....31168......15821727........8797534495.........4826926610498
..143...447343.....754700909.....1427843505563......2654271236904226
..528..6427791...35987024999...231638725420288...1458877292453477918
.1979.92387812.1716127952620.37582214286016391.801931987315155805350

Examples

			Some solutions for n=5 k=3
..0..0..1....0..1..0....0..0..1....0..0..1....0..0..1....0..0..1....0..1..0
..2..0..3....0..1..0....0..0..1....1..2..1....0..1..0....0..1..0....2..0..1
..3..1..1....1..2..1....2..3..2....1..3..2....2..2..1....2..2..1....0..2..1
..0..1..2....0..1..1....1..2..0....0..3..3....0..3..1....1..3..2....1..2..3
..1..2..0....3..3..0....1..0..0....0..1..3....0..1..0....0..1..0....3..0..0

Links

Crossrefs

Column 1 is A204678
Column 2 is A204679

A205310 T(n,k)=Number of nXk 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 2, 4, 15, 4, 12, 159, 159, 12, 40, 2191, 7445, 2191, 40, 143, 31168, 381958, 381958, 31168, 143, 528, 447343, 19490790, 70985206, 19490790, 447343, 528, 1979, 6427791, 996536552, 13049279920, 13049279920, 996536552, 6427791, 1979, 7466, 92387812
Offset: 1

Views

Author

R. H. Hardin Jan 25 2012

Keywords

Comments

Table starts
....1........2.............4................12.....................40
....2.......15...........159..............2191..................31168
....4......159..........7445............381958...............19490790
...12.....2191........381958..........70985206............13049279920
...40....31168......19490790.......13049279920..........8615950028840
..143...447343.....996536552.....2404472055439.......5705396521337690
..528..6427791...50933680120...442834241887042....3775750320744043966
.1979.92387812.2603456557653.81565593153176155.2499057571450100571862

Examples

			Some solutions for n=5 k=3
..0..0..1....0..0..1....0..0..1....0..1..0....0..0..1....0..0..1....0..1..1
..0..1..0....1..2..1....0..2..0....0..2..1....0..1..1....2..0..2....0..2..1
..2..2..1....1..3..2....3..1..1....1..0..0....2..0..2....2..1..1....1..1..0
..1..3..2....0..3..3....2..0..2....3..1..3....2..1..0....0..1..1....3..2..3
..0..1..0....0..1..3....0..1..0....0..1..0....3..2..2....2..2..3....3..0..0

Links

Crossrefs

Column 1 is A204678
Column 2 is A204679

A242472 T(n,k)=Number of length n+2 0..k arrays with no three equal elements in a row and new values 0..k introduced in 0..k order.

Original entry on oeis.org

3, 4, 5, 4, 11, 8, 4, 12, 30, 13, 4, 12, 40, 82, 21, 4, 12, 41, 143, 224, 34, 4, 12, 41, 158, 528, 612, 55, 4, 12, 41, 159, 663, 1979, 1672, 89, 4, 12, 41, 159, 684, 2944, 7466, 4568, 144, 4, 12, 41, 159, 685, 3204, 13537, 28246, 12480, 233, 4, 12, 41, 159, 685, 3232
Offset: 1

Views

Author

R. H. Hardin, May 15 2014

Keywords

Comments

Table starts
...3.....4......4.......4.......4.......4.......4.......4.......4.......4
...5....11.....12......12......12......12......12......12......12......12
...8....30.....40......41......41......41......41......41......41......41
..13....82....143.....158.....159.....159.....159.....159.....159.....159
..21...224....528.....663.....684.....685.....685.....685.....685.....685
..34...612...1979....2944....3204....3232....3233....3233....3233....3233
..55..1672...7466...13537...16042...16497...16533...16534...16534...16534
..89..4568..28246...63551...84412...90075...90817...90862...90863...90863
.144.12480.106992..301968..460174..520248..531812..532958..533013..533014
.233.34096.405481.1444795.2570411.3143900.3295779.3317613.3319308.3319374

Examples

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

Links

Crossrefs

Column 1 is A000045(n+3)
Column 2 is A021006(n-1)
Column 3 is A204678(n+2)
Column 4 is A222919(n+2)

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 2*a(n-1) +2*a(n-2)
k=3: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
k=4: a(n) = 7*a(n-1) -7*a(n-2) -20*a(n-3) +10*a(n-4) +24*a(n-5) +8*a(n-6)
k=5: [order 8]
k=6: [order 10]
k=7: [order 12]
k=8: [order 14]

A240629 T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 2, 4, 10, 4, 12, 109, 109, 12, 40, 1332, 4369, 1332, 40, 143, 16624, 180480, 180480, 16624, 143, 528, 208015, 7462748, 24648700, 7462748, 208015, 528, 1979, 2604059, 308596193, 3367163455, 3367163455, 308596193, 2604059, 1979, 7466, 32601488
Offset: 1

Views

Author

R. H. Hardin, Apr 09 2014

Keywords

Comments

Table starts
...1......2.........4...........12..............40.................143
...2.....10.......109.........1332...........16624..............208015
...4....109......4369.......180480.........7462748...........308596193
..12...1332....180480.....24648700......3367163455........459961775083
..40..16624...7462748...3367163455...1519699081714.....685854075788477
.143.208015.308596193.459961775083.685854075788477.1022628784514567961

Examples

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

Links

Crossrefs

Column 1 is A204678

Formula

Empirical for column k:
k=1: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4) for n>6
k=2: [order 10] for n>11
k=3: [order 46]
Showing 1-4 of 4 results.

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