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 1-9 of 9 results.

A183354 One quarter the number of nX2 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

4, 36, 144, 576, 2304, 9216, 36864, 147456, 589824, 2359296, 9437184, 37748736, 150994944, 603979776, 2415919104, 9663676416, 38654705664, 154618822656, 618475290624, 2473901162496, 9895604649984, 39582418599936, 158329674399744
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 2 of A183362

Examples

			Some solutions for 5X2 with a(1,1)=1
..1..1....1..3....1..2....1..3....1..3....1..2....1..4....1..2....1..3....1..3
..4..2....4..2....4..4....4..4....4..2....1..2....3..3....4..3....2..2....4..3
..3..3....4..2....3..3....3..2....4..1....4..4....2..2....2..1....4..1....4..2
..1..1....3..1....1..1....1..2....2..3....2..3....1..1....2..1....4..1....3..2
..2..4....2..1....2..2....1..3....1..3....1..1....4..4....3..4....2..3....3..1

Links

Formula

Empirical: a(n)=4*a(n-1) = A002063(n-1) for n>2

A183355 One quarter the number of nX3 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

12, 144, 432, 1296, 3888, 11664, 34992, 104976, 314928, 944784, 2834352, 8503056, 25509168, 76527504, 229582512, 688747536, 2066242608, 6198727824, 18596183472, 55788550416, 167365651248, 502096953744, 1506290861232, 4518872583696
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 3 of A183362

Examples

			Some solutions for 5X3 with a(1,1)=1
..1..1..4....1..1..2....1..4..2....1..2..4....1..1..4....1..3..3....1..2..4
..4..2..2....2..4..3....1..3..2....4..2..1....3..2..4....2..4..1....1..2..4
..3..3..1....2..4..3....2..3..4....4..3..3....3..2..1....2..4..1....3..3..1
..2..4..4....1..1..2....2..1..4....2..1..4....4..4..3....1..3..2....2..4..1
..1..1..3....4..3..2....4..1..3....3..1..4....2..1..3....1..3..2....1..4..2

Links

Formula

Empirical: a(n)=3*a(n-1) for n>2

A183356 One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

36, 576, 1296, 3600, 9216, 24336, 63504, 166464, 435600, 1140624, 2985984, 7817616, 20466576, 53582400, 140280336, 367258896, 961496064, 2517229584, 6590192400, 17253347904, 45169851024, 118256205456, 309598765056, 810540090000
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Column 4 of A183362.

Examples

			Some solutions for 5 X 4 with a(1,1)=1:
  1 4 3 3    1 1 4 4    1 2 4 1    1 4 2 2    1 1 3 4
  2 4 1 1    4 2 3 1    3 2 4 1    1 4 3 3    2 2 3 1
  3 3 2 2    4 2 3 1    4 1 3 3    3 2 1 1    3 4 4 2
  1 1 4 4    3 1 4 4    4 1 2 2    3 2 4 4    3 1 1 3
  4 2 3 1    3 1 2 2    2 3 4 1    1 1 3 2    4 2 2 4

Links

Crossrefs

Cf. A183362.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.
Conjectures from Colin Barker, Mar 28 2018: (Start)
G.f.: 36*x*(1 + 14*x + 2*x^2 - 3*x^3) / ((1 + x)*(1 - 3*x + x^2)).
a(n) = (9/5)*2^(3-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.
(End)
Assuming Colin Barker's conjectures, a(n) = (12*Fibonacci(n+1))^2, n>1. - Ehren Metcalfe, Apr 21 2018

A183357 One quarter the number of n X 5 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

108, 2304, 3888, 9216, 24192, 57600, 137088, 331776, 802944, 1937664, 4675968, 11289600, 27257472, 65804544, 158864256, 383533056, 925932672, 2235398400, 5396727168, 13028852736, 31454434944, 75937722624, 183329877888
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Column 5 of A183362.

Examples

			Some solutions for 7 X 5 with a(1,1)=1:
..1..1..2..4..1....1..2..2..3..3....1..2..2..3..3....1..1..3..4..1
..4..3..3..4..2....1..4..4..1..2....3..4..4..1..1....4..2..2..4..3
..2..2..1..1..3....2..3..3..1..2....2..1..3..2..2....3..3..1..1..2
..3..4..4..2..3....4..1..2..4..4....2..1..3..4..4....2..4..4..3..2
..1..1..3..2..1....3..1..2..3..3....3..4..2..1..1....1..1..2..3..1
..4..2..3..4..4....2..4..4..1..2....3..4..2..3..3....4..3..2..4..1
..3..2..1..1..2....2..3..3..1..4....2..1..1..4..2....2..3..1..4..2

Links

Crossrefs

Cf. A183362.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) for n>7.
Empirical g.f.: 36*x*(3 + 58*x - 20*x^2 + 34*x^3 + 29*x^4 - 24*x^5 - 12*x^6) / ((1 + x^2)*(1 - 2*x - x^2)). - Colin Barker, Mar 28 2018

A183358 One quarter the number of nX6 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

324, 9216, 11664, 24336, 57600, 147456, 331776, 746496, 1679616, 3873024, 8856576, 20358144, 46457856, 106502400, 243360000, 557715456, 1275346944, 2921186304, 6682081536, 15300700416, 35007906816, 80147874816, 183403201536
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 6 of A183362

Examples

			Some solutions for 5X6 with a(1,1)=1
..1..3..4..1..1..4....1..4..2..3..1..4....1..1..3..4..1..3....1..2..4..4..1..3
..2..3..4..2..3..3....2..4..1..3..2..4....3..2..2..4..1..2....3..3..1..2..2..3
..2..1..1..2..4..1....2..3..1..4..2..1....4..4..1..3..3..4....4..4..1..3..4..4
..4..4..3..3..4..2....1..3..2..4..3..1....2..3..1..2..2..4....1..2..2..3..1..1
..1..2..2..1..1..3....1..4..2..1..3..2....2..3..4..4..1..1....1..3..4..4..2..3

Links

Formula

Empirical: a(n)=2*a(n-1)+2*a(n-2)-4*a(n-3)+4*a(n-4)-4*a(n-5)+2*a(n-6)-6*a(n-7)+a(n-10) for n>14

A183359 One quarter the number of nX7 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

972, 36864, 34992, 63504, 137088, 331776, 829440, 1806336, 3852288, 8294400, 18137088, 40144896, 88897536, 196448256, 433465344, 955551744, 2106667008, 4645785600, 10246588416, 22600912896, 49849804800, 109947949056
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 7 of A183362

Examples

			Some solutions for 5X7 with a(1,1)=1
..1..1..2..3..1..2..2....1..1..3..4..2..1..1....1..2..3..4..1..1..3
..2..4..4..3..1..4..4....2..4..3..1..2..4..3....3..2..1..4..3..2..2
..2..3..1..2..2..3..3....3..4..2..1..3..4..2....3..4..1..2..3..4..4
..4..3..1..4..4..1..1....3..1..2..4..3..1..2....2..4..3..2..1..1..3
..4..2..2..3..3..2..2....2..1..3..4..2..1..4....1..1..3..4..4..2..2

Links

Formula

Empirical: a(n)=2*a(n-1)+a(n-3)-2*a(n-4)+4*a(n-5)+a(n-6)-a(n-9) for n>14

A183360 One quarter the number of nX8 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

2916, 147456, 104976, 166464, 331776, 746496, 1806336, 4460544, 9437184, 19501056, 40144896, 84934656, 180633600, 391090176, 840536064, 1816805376, 3893760000, 8387629056, 17960288256, 38654705664, 82833444864, 178259595264
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 8 of A183362

Examples

			Some solutions for 5X8 with a(1,1)=1
..1..2..2..3..1..2..2..1....1..2..4..4..1..2..4..4....1..3..4..1..2..2..4..3
..1..3..4..4..1..3..4..4....1..3..3..2..1..3..3..2....2..2..4..1..3..3..4..1
..4..3..1..2..2..3..1..2....4..4..1..2..4..4..1..2....4..1..3..2..4..1..2..2
..2..2..1..3..4..4..1..2....2..2..1..3..3..2..1..3....4..1..3..2..4..1..3..3
..3..4..4..3..1..2..3..4....3..3..4..4..1..2..4..4....2..2..4..1..3..2..4..1

Links

A183361 One quarter the number of nX9 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

8748, 589824, 314928, 435600, 802944, 1679616, 3852288, 9437184, 23003136, 47775744, 95551488, 191102976, 389283840, 807469056, 1695744000, 3588489216, 7596343296, 16057958400, 33888927744, 71430045696, 150473539584
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Column 9 of A183362

Examples

			Some solutions for 5X9 with a(1,1)=1
..1..1..2..3..3..1..2..3..4....1..1..2..4..4..2..2..3..1
..2..4..4..1..2..4..4..1..1....2..4..3..3..1..1..4..3..2
..2..3..3..1..2..3..3..2..2....2..4..1..2..2..3..4..1..2
..4..1..2..4..4..1..1..4..3....3..3..1..4..4..3..2..1..3
..3..1..2..3..3..2..2..4..1....4..2..2..3..1..1..2..4..4

Links

A183353 One quarter the number of n X n 1..4 arrays with no two neighbors of any element equal to each other.

Original entry on oeis.org

1, 36, 432, 3600, 24192, 147456, 829440, 4460544, 23003136, 115605504, 566231040, 2727346176, 12910067712
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Diagonal of A183362

Examples

			Some solutions for 5X5 with a(1,1)=1
..1..3..2..2..4....1..2..3..1..4....1..3..3..2..2....1..1..3..4..2
..2..4..1..3..4....1..4..3..2..4....1..2..4..4..3....3..2..2..4..1
..3..4..1..3..2....3..4..1..2..3....3..2..1..1..3....4..4..1..3..3
..1..2..2..4..1....2..2..1..4..3....4..4..3..2..4....2..3..1..2..2
..4..3..3..4..1....1..3..3..4..1....1..1..3..2..1....1..3..4..4..1
Showing 1-9 of 9 results.

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