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 1-8 of 8 results.

A183519 Number of nX2 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

3, 9, 31, 95, 309, 911, 2803, 8673, 26619, 81959, 252477, 777327, 2393627, 7371657, 22698115, 69895583, 215235669, 662786215, 2040959827, 6284869089, 19353386043, 59596135287, 183518286189, 565119695167, 1740209766219, 5358741068409
Offset: 1

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Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 2 of A183526

Examples

			Some solutions for 3X2
..1..2....0..2....2..1....2..0....0..2....2..2....1..0....1..0....0..1....1..2
..0..1....1..2....1..2....0..2....1..2....0..0....1..2....1..2....2..1....2..1
..1..2....2..1....0..2....0..0....0..2....1..1....1..0....2..1....1..2....2..0
		

Formula

Empirical: a(n)=3*a(n-1)+6*a(n-3)-16*a(n-4)+7*a(n-6)-25*a(n-7)-44*a(n-9)+102*a(n-10)-184*a(n-12)+520*a(n-13)+320*a(n-15)-720*a(n-16)+640*a(n-18)-1600*a(n-19)

A183520 Number of n X 3 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

5, 31, 101, 543, 2233, 10003, 47685, 215451, 994397, 4603823, 21240401, 98257363, 454235165, 2100740935, 9717553917, 44943606231, 207898873245, 961691911899, 4448501263357, 20578124472715, 95191234404373, 440340646073843
Offset: 1

Views

Author

R. H. Hardin, Jan 05 2011

Keywords

Examples

			Some solutions for 5X3
..2..0..2....2..0..2....2..1..0....0..1..1....2..2..1....1..0..1....2..0..2
..0..2..0....1..2..2....2..2..2....2..1..2....2..2..2....2..1..2....0..2..1
..2..1..2....0..2..0....1..1..2....0..1..0....1..0..1....0..0..0....2..1..0
..2..0..2....0..2..2....2..2..2....2..2..1....2..2..2....2..2..1....2..0..1
..0..1..0....2..1..0....0..1..2....0..1..2....1..2..2....1..2..2....0..0..1
		

Crossrefs

Column 3 of A183526.

Programs

  • Maple
    Configs:= map(t -> convert(t+3^6, base, 3)[1..6],[$0..3^6-1]):
    q:= proc(a,b) local A,B;
       A:= Configs[a]; B:= Configs[b];
       if A[4..6]<> B[1..3] then return 0 fi;
       if A[4] <> A[1]+A[5]+B[4] mod 3  and A[4] <> A[2]+B[5] mod 3 then return 0 fi;
       if A[5] <> A[2]+A[4]+A[6]+B[5] mod 3 and A[5] <> A[1]+A[3]+B[4]+B[6] mod 3 then return 0 fi;
       if A[6] <> A[3]+A[5]+B[6] mod 3 and A[6] <> A[2]+B[5] mod 3 then return 0 fi;
       1
    end proc:
    T:= Matrix(3^6,3^6, q):
    u:= Vector[row](3^6,proc(a) if Configs[a][1..3]=[0,0,0] then 1 else 0 fi end proc):
    v:= Vector(3^6,proc(a) if Configs[a][4..6]=[0,0,0] then 1 else 0 fi end proc):
    V[0]:= v:
    for nn from 1 to 30 do V[nn]:= T . V[nn-1] od:
    seq(u . V[n],n=1..30); # Robert Israel, Nov 17 2019

Formula

Linear recurrence of order 156: see links. - Robert Israel, Nov 17 2019

A183521 Number of nX4 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

7, 95, 543, 3507, 27609, 201833, 1521573, 11678037, 89238523, 683029435, 5235031077, 40141122349, 307807564417, 2360732530937, 18105826441313, 138867315400205, 1065099011259479, 8169267911756541, 62658120915577663
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 4 of A183526

Examples

			Some solutions for 3X4
..2..1..2..1....2..1..0..1....1..1..2..2....2..1..0..0....0..0..2..0
..1..1..0..2....2..2..1..0....0..1..2..0....1..2..2..0....1..0..2..1
..1..2..0..2....1..2..2..1....1..1..2..2....0..2..0..2....2..1..2..2
		

A183522 Number of nX5 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

13, 309, 2233, 27609, 371691, 4406933, 56562977, 728459961, 9260503697, 118800214951, 1524147275433, 19534446701521, 250583781238959, 3214379129443263, 41229745589418633, 528882044555348133
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 5 of A183526

Examples

			Some solutions for 3X5
..2..2..1..0..2....0..2..0..0..0....2..1..1..2..1....0..1..0..0..1
..0..2..0..2..0....1..2..0..1..0....1..0..0..1..2....2..1..0..2..1
..1..1..1..2..2....0..2..0..0..1....0..0..0..0..2....0..1..0..0..1
		

A183518 Number of n X n 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

1, 9, 101, 3507, 371691, 89738569
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Diagonal of A183526

Examples

			Some solutions for 3X3
..0..0..2....2..2..2....1..1..1....0..0..0....0..1..0....2..0..0....1..2..0
..0..2..0....0..1..0....1..1..0....0..1..0....2..1..2....2..0..1....1..1..1
..0..0..0....0..0..0....1..0..1....1..0..0....1..1..0....0..0..1....0..2..0
		

A183523 Number of nX6 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

23, 911, 10003, 201833, 4406933, 89738569, 1908431611
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 6 of A183526

Examples

			Some solutions for 3X6
..2..1..0..0..2..2....1..1..0..1..0..1....0..2..1..1..0..2....0..2..2..0..1..2
..0..2..0..1..2..1....0..1..1..1..1..0....1..1..2..0..0..2....0..0..0..0..1..1
..2..1..0..0..2..0....1..1..2..1..1..1....1..2..0..2..2..1....0..1..1..0..2..1
		

A183524 Number of nX7 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

37, 2803, 47685, 1521573, 56562977, 1908431611
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 7 of A183526

Examples

			Some solutions for 3X7
..0..2..1..1..2..1..1....2..0..2..1..0..2..2....2..0..2..1..0..2..0
..1..0..1..1..2..1..0....2..0..1..0..0..0..0....2..0..1..0..0..0..2
..0..2..2..2..2..1..1....0..0..2..1..0..1..1....1..2..1..1..0..0..0
		

A183525 Number of nX8 0..2 arrays with each element equal to either the sum mod 3 of its horizontal and vertical neighbors or the sum mod 3 of its diagonal and antidiagonal neighbors.

Original entry on oeis.org

63, 8673, 215451, 11678037, 728459961
Offset: 1

Views

Author

R. H. Hardin Jan 05 2011

Keywords

Comments

Column 8 of A183526

Examples

			Some solutions for 3X8
..0..2..2..2..1..0..0..1....0..1..1..1..0..1..1..0....0..0..0..1..0..0..1..0
..1..0..1..2..2..1..1..2....2..1..2..0..1..2..0..0....2..0..2..1..1..2..0..2
..0..2..0..0..2..0..1..0....0..1..0..0..2..0..2..2....1..2..1..2..0..1..0..2
		
Showing 1-8 of 8 results.