

A204560


Symmetric matrix: f(i,j)=floor[(2i+2j+4)/4]floor[(i+j+2)/4], by (constant) antidiagonals.


3



1, 1, 1, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
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OFFSET

1,4


COMMENTS

For n>=2, the number of occurrences of n is 16n14. For a guide to related sequences and permanents, see A204551.
Northwest corner:
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
3 3 3 3 4 4 4 4 5
3 3 3 4 4 4 4 5 5
f[i_, j_] := Floor[(2 i + 2 j + 4)/4]  Floor[(i + j + 2)/4];
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, 14}, {i, 1, n}]] (* A204560 *)
Permanent[m_] :=
With[{a = Array[x, Length[m]]},
Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 15}] (* A204561 *)
Cf. A204561, A204551.
tabl


LINKS

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


CROSSREFS

Sequence in context: A176170 A062153 A217693 * A135661 A082998 A076620
Adjacent sequences: A204557 A204558 A204559 * A204561 A204562 A204563


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jan 16 2012


STATUS

approved



