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A204551 Symmetric matrix: f(i,j)=floor[(2i+2j+1)/4]-floor[(i+j)/4], by (constant) antidiagonals. 8
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

For n>=1, the number of occurrences of n is 16n-6.  In the following guide to related matrices and permanents, Duvwxyz represents the matrix remaining after row 1 of the matrix Auvwxyz is deleted:

Matrix...............Permanent of n-th submatrix

A204551..............A204552

A204553=D204551......A204554

A204560=D204553......A204561

A204562=D204560......A204563

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

Northwest corner:

1 1 1 1 2 2 2 2 3

1 1 1 2 2 2 2 3 3

1 1 2 2 2 2 3 3 3

1 2 2 2 2 3 3 3 3

2 2 2 2 3 3 3 3 4

2 2 2 3 3 3 3 4 4

2 3 3 3 3 4 4 4 4

MATHEMATICA

f[i_, j_] :=

Floor[(2 i + 2 j + 1)/4] - Floor[(i + j)/4];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[16]] (* 8x8 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 14}, {i, 1, n}]]    (* A204551 *)

Permanent[m_] :=

  With[{a = Array[x, Length[m]]},

   Coefficient[Times @@ (m.a), Times @@ a]];

Table[Permanent[m[n]], {n, 1, 15}]  (* A204552 *)

CROSSREFS

Cf. A204551, A204296.

Sequence in context: A121902 A087103 A287091 * A211661 A111972 A073458

Adjacent sequences:  A204548 A204549 A204550 * A204552 A204553 A204554

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 16 2012

STATUS

approved

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Last modified June 28 08:22 EDT 2017. Contains 288813 sequences.