|
%I #7 Jun 29 2017 15:54:39
%S 1,3,3,5,6,5,7,9,9,7,9,12,13,12,9,11,15,17,17,15,11,13,18,21,22,21,18,
%T 13,15,21,25,27,27,25,21,15,17,24,29,32,33,32,29,24,17,19,27,33,37,39,
%U 39,37,33,27,19,21,30,37,42,45,46,45,42,37,30,21,23,33,41,47
%N Symmetric matrix read by antidiagonals given by T(i,j)=i*j+i+j-2.
%H David Singmaster, David Fielker, N. J. A. Sloane, <a href="/A004116/a004116.pdf">Correspondence, August 1979</a>
%e Northwest corner:
%e 1...3...5....7....9
%e 3...6...9....12...15
%e 5...9...13...17...21
%e 7...12..17...22...27
%t f[i_, j_] := i*j + i + j - 2;
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[5]] (* 5x5 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 12}, {i, 1, n}]] (* A204250 *)
%t Permanent[m_] :=
%t With[{a = Array[x, Length[m]]},
%t Coefficient[Times @@ (m.a), Times @@ a]];
%t Table[Permanent[m[n]], {n, 1, 14}] (* A204251 *)
%Y Cf. A204251.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Jan 14 2012
|
