A353452
a(n) is the determinant of the n X n symmetric matrix M(n) that is defined as M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
Original entry on oeis.org
1, 0, -1, 0, 1, -4, 12, 64, -172, -1348, 3456, 34240, -87084, 370640, -872336, -22639616, 52307088, -181323568, 399580288, 23627011200, -51305628400, -686160247552, 1545932859328, 68098264912128, -155370174372864, 6326621032802304, -13829529077133312, -1087288396552040448
Offset: 0
a(8) = -172:
0, 1, 0, 0, 0, 0, 0, 0;
1, 0, 1, 2, 0, 0, 0, 0;
0, 1, 0, 1, 2, 3, 0, 0;
0, 2, 1, 0, 1, 2, 3, 4;
0, 0, 2, 1, 0, 1, 2, 3;
0, 0, 3, 2, 1, 0, 1, 2;
0, 0, 0, 3, 2, 1, 0, 1;
0, 0, 0, 4, 3, 2, 1, 0.
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Join[{1},Table[Det[Table[If[Min[i,j]
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a(n) = matdet(matrix(n, n, i, j, if ((min(i,j) < max(i,j)) && (max(i,j) <= 2*min(i,j)), abs(i-j)))); \\ Michel Marcus, Apr 20 2022
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from sympy import Matrix
def A353452(n): return Matrix(n, n, lambda i, j: abs(i-j) if min(i,j)Chai Wah Wu, Aug 29 2023
A353453
a(n) is the permanent of the n X n symmetric matrix M(n) that is defined as M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
Original entry on oeis.org
1, 0, 1, 0, 1, 4, 64, 576, 7844, 63524, 882772, 11713408, 252996564, 5879980400, 184839020672, 5698866739200, 229815005974352, 9350598794677712, 480306381374466176, 23741710999960266176, 1446802666239931811472, 86153125248221968292928, 6197781268948296566634304
Offset: 0
a(8) = 7844:
0, 1, 0, 0, 0, 0, 0, 0;
1, 0, 1, 2, 0, 0, 0, 0;
0, 1, 0, 1, 2, 3, 0, 0;
0, 2, 1, 0, 1, 2, 3, 4;
0, 0, 2, 1, 0, 1, 2, 3;
0, 0, 3, 2, 1, 0, 1, 2;
0, 0, 0, 3, 2, 1, 0, 1;
0, 0, 0, 4, 3, 2, 1, 0.
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Join[{1},Table[Permanent[Table[If[Min[i,j]
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a(n) = matpermanent(matrix(n, n, i, j, if ((min(i,j) < max(i,j)) && (max(i,j) <= 2*min(i,j)), abs(i-j)))); \\ Michel Marcus, Apr 20 2022
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from sympy import Matrix
def A353453(n): return Matrix(n, n, lambda i, j: abs(i-j) if min(i,j)Chai Wah Wu, Aug 29 2023
A357420
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
Original entry on oeis.org
1, 1, 1, 8, 86, 878, 13730, 348760, 11622396, 509566864, 26894616012, 1701189027944, 125492778658096, 10738546182981256, 1049631636279244832, 117756049412699967072
Offset: 0
a(4) = 86:
0, 1, 0, 0, 0, 0, 0, 0;
1, 0, 1, 2, 0, 0, 0, 0;
0, 1, 0, 1, 2, 3, 0, 0;
0, 2, 1, 0, 1, 2, 3, 4;
0, 0, 2, 1, 0, 1, 2, 3;
0, 0, 3, 2, 1, 0, 1, 2;
0, 0, 0, 3, 2, 1, 0, 1;
0, 0, 0, 4, 3, 2, 1, 0.
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M[i_, j_, n_] := If[Min[i, j] < Max[i, j] <= 2 Min[i, j], Abs[j - i], 0]; a[n_] := Sum[Product[M[Part[PermutationList[s, 2 n], 2 i - 1], Part[PermutationList[s, 2 n], 2 i], 2 n], {i, n}], {s, SymmetricGroup[2 n] // GroupElements}]/(n!*2^n); Array[a, 6, 0]
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