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 1-5 of 5 results.

A222834 Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

7, 96, 216, 600, 1536, 4056, 10584, 27744, 72600, 190104, 497664, 1302936, 3411096, 8930400, 23380056, 61209816, 160249344, 419538264, 1098365400, 2875557984, 7528308504, 19709367576, 51599794176, 135090015000, 353670250776
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2013

Keywords

Comments

Column 4 of A222838.

Examples

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

Links

Crossrefs

Cf. A222838.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.
Conjectures from Colin Barker, Aug 16 2018: (Start)
G.f.: x*(7 + 82*x + 10*x^2 - 17*x^3) / ((1 + x)*(1 - 3*x + x^2)).
a(n) = (3/5)*2^(2-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.
(End)

A222835 Number of n X 5 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

19, 384, 648, 1536, 4032, 9600, 22848, 55296, 133824, 322944, 779328, 1881600, 4542912, 10967424, 26477376, 63922176, 154322112, 372566400, 899454528, 2171475456, 5242405824, 12656287104, 30554979648, 73766246400, 178087472832
Offset: 1

Views

Author

R. H. Hardin, Mar 06 2013

Keywords

Comments

Column 5 of A222838.

Examples

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

Links

Crossrefs

Cf. A222838.

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) for n>7.
Conjectures from Colin Barker, Aug 16 2018: (Start)
G.f.: x*(19 + 346*x - 120*x^2 + 202*x^3 + 173*x^4 - 144*x^5 - 72*x^6) / ((1 + x^2)*(1 - 2*x - x^2)).
a(n) = 48*((-1+i)*((-i)^n+i^(1+n)) + (1-sqrt(2))^n + (1+sqrt(2))^n) for n>3, where i=sqrt(-1).
(End)

A222836 Number of nX6 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

55, 1536, 1944, 4056, 9600, 24576, 55296, 124416, 279936, 645504, 1476096, 3393024, 7742976, 17750400, 40560000, 92952576, 212557824, 486864384, 1113680256, 2550116736, 5834651136, 13357979136, 30567200256, 69973632384, 160134620544
Offset: 1

Views

Author

R. H. Hardin Mar 06 2013

Keywords

Comments

Column 6 of A222838

Examples

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

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

A222837 Number of nX7 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

163, 6144, 5832, 10584, 22848, 55296, 138240, 301056, 642048, 1382400, 3022848, 6690816, 14816256, 32741376, 72244224, 159258624, 351111168, 774297600, 1707764736, 3766818816, 8308300800, 18324658176, 40416165888, 89140107264
Offset: 1

Views

Author

R. H. Hardin Mar 06 2013

Keywords

Comments

Column 7 of A222838

Examples

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

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

A222833 Number of n X n 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 7, 72, 600, 4032, 24576, 138240, 743424, 3833856, 19267584, 94371840, 454557696
Offset: 1

Views

Author

R. H. Hardin Mar 06 2013

Keywords

Comments

Diagonal of A222838

Examples

			Some solutions for n=4
..0..1..1..2....0..1..1..0....0..1..2..2....0..1..2..0....0..1..2..3
..3..2..0..0....0..2..3..3....2..3..3..0....0..3..3..0....3..1..2..3
..1..2..3..1....1..2..0..1....2..0..1..1....2..2..1..1....2..0..0..1
..0..0..3..1....1..3..0..1....1..0..2..2....3..0..0..2....2..3..3..2
Showing 1-5 of 5 results.

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