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A204545 Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals. 3

%I #6 Mar 30 2012 18:58:08

%S 1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0

%N Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.

%C A block matrix over {0,1}. For a guide to related matrices and permanents, see A204269 and A204453.

%e Northwest corner:

%e 1 0 0 1 1 0 0 1

%e 0 0 1 1 0 0 1 1

%e 0 1 1 0 0 1 1 0

%e 1 1 0 0 1 1 0 0

%e 1 0 0 1 1 0 0 1

%e 0 0 1 1 0 0 1 1

%e 0 1 1 0 0 1 1 0

%e 1 1 0 0 1 1 0 0

%t f[i_, j_] := Floor[(i + j + 3)/4] - Floor[(i + j + 1)/4];

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

%t TableForm[m[8]] (* 8x8 principal submatrix *)

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

%t {n, 1, 14}, {i, 1, n}]] (* A204545 *)

%t Permanent[m_] :=

%t With[{a = Array[x, Length[m]]},

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

%t Table[Permanent[m[n]], {n, 1, 22}] (* A204546 *)

%Y Cf. A204546, A204296.

%K nonn,tabl

%O 1

%A _Clark Kimberling_, Jan 16 2012

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)