A204238 -id:A204238 - cp's OEIS frontend

A204237 Symmetric matrix given by f(i,j)=max(3i-j,3j-i).

2, 5, 5, 8, 4, 8, 11, 7, 7, 11, 14, 10, 6, 10, 14, 17, 13, 9, 9, 13, 17, 20, 16, 12, 8, 12, 16, 20, 23, 19, 15, 11, 11, 15, 19, 23, 26, 22, 18, 14, 10, 14, 18, 22, 26, 29, 25, 21, 17, 13, 13, 17, 21, 25, 29, 32, 28, 24, 20, 16, 12, 16, 20, 24, 28, 32, 35, 31, 27, 23

Offset: 1

Clark Kimberling, Jan 13 2012

			Northwest corner:
2....5....8....11...14...17
5....4....7....10...13...16
8....7....6....9....12...15
11...10...9....8....11...14
14...13...12...11...10...13

Cf. A204238, A204239.

f[i_, j_] := Max[3 i - j, 3 j - i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]  (* A204237 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)

A204239 Permanent of the n-th principal submatrix of A204237.

Original entry on oeis.org

2, 33, 1112, 69908, 6960472, 1010678724, 201542214592, 52862893123648, 17646889124736128, 7306075691359891008, 3673978840975236778496, 2205779786212911066883328, 1558502652244224074264296960

Offset: 1

Clark Kimberling, Jan 13 2012

nonn

Cf. A204237, A204238.

f[i_, j_] := Max[3 i - j, 3 j - i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]     (* A204237 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)

A204243 Determinant of the n-th principal submatrix of A204242.

Original entry on oeis.org

1, 2, 11, 144, 4149, 251622, 31340799, 7913773980, 4024015413705, 4106387069191890, 8395359475529822355, 34357677843892688699400, 281336437060919094044274525, 4608419756389534634440592965950, 150992374805715685629827976712244775

Offset: 1

Clark Kimberling, Jan 13 2012

nonn

Colin Barker, Table of n, a(n) for n = 1..80
Wikipedia, Matrix determinant lemma

Cf. A005329, A203011, A204238, A204242.

f:= n -> (1 - add(1/(2^i-1),i=2..n))*mul(2^i-1,i=2..n):
seq(f(n),n=1..30); # Robert Israel, Nov 30 2015

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := 2^i - 1;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]     (* A204242 *)
Table[Det[m[n]], {n, 1, 15}]  (* A204243 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}]   (* A203011 *)

vector(20, n, matdet(matrix(n, n, i, j, if(i==1, 1, if(j==1, 1, if(i==j, 2^i-1)))))) \\ Colin Barker, Nov 27 2015

a(n) = (1 - Sum_{k=2..n} 1/(2^k-1)) * Product_{k=2..n} (2^k-1) = 2*A005329(n) - A203011(n). - Robert Israel, Nov 30 2015

cp's OEIS Frontend

A204237 Symmetric matrix given by f(i,j)=max(3i-j,3j-i).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A204239 Permanent of the n-th principal submatrix of A204237.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A204243 Determinant of the n-th principal submatrix of A204242.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula