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A204423 Infinite matrix: f(i,j)=(2i+j mod 3), by antidiagonals. 3

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

%S 0,1,2,2,0,1,0,1,2,0,1,2,0,1,2,2,0,1,2,0,1,0,1,2,0,1,2,0,1,2,0,1,2,0,

%T 1,2,2,0,1,2,0,1,2,0,1,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,2,0,

%U 1,2,0,1,2,0,1,2,0,1,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2

%N Infinite matrix: f(i,j)=(2i+j mod 3), by antidiagonals.

%C An infinite block matrix over {0,1,2}. See A204263 for a guide to related matrices and permanents.

%e Northwest corner:

%e 0 1 2 0 1 2

%e 2 0 1 2 0 1

%e 1 2 0 1 2 0

%e 0 1 2 0 1 2

%e 2 0 1 2 0 1

%e 1 2 0 1 2 0

%t f[i_, j_] := Mod[2 i + j, 3];

%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}]] (* A204423 *)

%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}] (* A204424 *)

%Y Cf. A204424, A204263.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Jan 15 2012

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)