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%I A363460 #19 Jun 08 2023 08:52:20
%S A363460 1,1,11,556,74964,21700112,11500685084,10057140949968,
%T A363460 13496937368200000,26331147893897760544,71606290155732170272320,
%U A363460 262516365211410942628577408,1262517559940020030446967822592,7786463232979127181938238723356160,60414239829783205320232261233394491136
%N A363460 a(n) is the permanent of the n X n matrix formed by placing 1..n^2 in L-shaped gnomons in alternating directions.
%C A363460 The matrix is the upper-left n X n part of the square arrangement in A081344.
%C A363460 The matrix element k is at row A220604(k) and column A220603(k), for k = 1..n^2.
%e A363460 a(5) = 21700112 is the permanent of the 5 X 5 matrix
%e A363460 | 1----2 9---10 25 |
%e A363460 | | | | | |
%e A363460 | 4----3 8 11 24 |
%e A363460 | | | | | |
%e A363460 | 5----6----7 12 23 |
%e A363460 | | | |
%e A363460 | 16---15---14---13 22 |
%e A363460 | | | |
%e A363460 | 17---18---19---20---21 |
%t A363460 a={1}; For[n=1, n<=14, n++,k=i=j=1; M[i,j]=k++; For[h=1, h<n, h++, If[i==j==1, M[i,++j]=k++;For[c=1, c<=h, c++, M[++i,j]=k++; M[i, --j]=k++], If[j==1 && i!=1, M[++i, j]=k++; For[c=1, c<=h, c++, M[i, ++j]=k++];For[c=1, c<=h, c++, M[--i, j]=k++], If[i==1 &&j!=1, M[i, ++j]=k++; For[c=1, c<=h, c++, M[++i, j]=k++]; For[c=1, c<=h, c++, M[i, --j]=k++]]]]];AppendTo[a, Permanent[Table[M[i, j], {i, n}, {j, n}]]]]; a
%Y A363460 Cf. A006527 (trace), A037270 (elements sum of the matrix), A060736, A061349 (anti trace), A081344, A220603, A220604, A363376 (determinant).
%K A363460 nonn
%O A363460 0,3
%A A363460 _Stefano Spezia_, Jun 03 2023