A383772
a(n) = neg(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (1, 2, ... , n), and neg(M(n)) is the negative part of the determinant of M(n); see A380661.
Original entry on oeis.org
0, -4, -18, -610, -15675, -772122, -47282844, -3918873376, -410168886615, -53329052728000, -8417451284317614, -1586200451151892608, -351735180091505203539, -90667510133054591492224, -26884188746929397888775000, -9086147134545912835276742656
Offset: 1
The rows of M(4) are (1, 2, 3, 4), (4, 1, 2, 3), (3, 4, 1, 2), (2, 3, 4, 1); determinant(M(4)) = -160; permanent(M(4)) = 1060, so neg(M(4)) = (-160 - 1060)/2 = -610 and pos(M(4)) = (-160 + 1060)/2 = 450.
-
z = 18;
v[n_] := Table[k + 1, {k, 0, n - 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]];
p = Table[Simplify[Permanent[u[n]]], {n, 1, z}] (* A085719 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A052182 *)
neg = (d - p)/2 (* A383772 *)
pos = (d + p)/2 (* A383773 *)
A383774
a(n) = neg(M(n)), where M(n) is the n X n left circulant matrix with (row 1) = (1, 2, ... , n), and neg(M(n)) is the negative part of the determinant of M(n); see A380661.
Original entry on oeis.org
0, -4, -36, -450, -15675, -772122, -47753440, -3909436192, -410168886615, -53329052728000, -8417606908865220, -1586195621597483136, -351735180091505203539, -90667510133054591492224, -26884188980472806091900000, -9086147124746080046118543360
Offset: 1
The rows of M(4) are (1, 2, 3, 4), (2, 3, 4, 1), (3, 4, 1, 2), (4, 1, 2, 3); determinant(M(4)) = 160; permanent(M(4)) = 1060, so neg(M(4)) = (160 - 1060)/2 = -450 and pos(M(4)) = (160 + 1060)/2 = 610.
-
z = 18;
v[n_] := Table[k + 1, {k, 0, n - 1}];
u[n_] := Table[RotateLeft[#, k - 1], {k, 1, Length[#]}] &[v[n]];
p = Table[Simplify[Permanent[u[n]]], {n, 1, z}] (* A085719 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A052182, with altered signs *)
neg = (d - p)/2 (* A383774 *)
pos = (d + p)/2 (* A383775 *)
A383775
a(n) = pos(M(n)), where M(n) is the n X n left circulant matrix with (row 1) = (1, 2, ... , n), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.
Original entry on oeis.org
1, 1, 18, 610, 17550, 744906, 47282844, 3918873376, 410384120220, 53323552728000, 8417451284317614, 1586200451151892608, 351735343178101060906, 90667504180193792086144, 26884188746929397888775000, 9086147134545912835276742656, 3472279409772212369077001352888
Offset: 1
The rows of M(4) are (1, 2, 3, 4), (2, 3, 4, 1), (3, 4, 1, 2), (4, 1, 2, 3); determinant(M(4)) = 160; permanent(M(4)) = 1060, so neg(M(4)) = (160 - 1060)/2 = -450 and pos(M(4)) = (160 + 1060)/2 = 610.
-
z = 18;
v[n_] := Table[k + 1, {k, 0, n - 1}];
u[n_] := Table[RotateLeft[#, k - 1], {k, 1, Length[#]}] &[v[n]];
p = Table[Simplify[Permanent[u[n]]], {n, 1, z}] (* A085719 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A052182, with altered signs *)
neg = (d - p)/2 (* A383774 *)
pos = (d + p)/2 (* A383775 *)
Showing 1-3 of 3 results.