A384079
a(n) = permanent of the n X n circulant matrix with (row 1) = (F(0), F(1), ..., F(n-1)), where F = A000045 (Fibonacci numbers).
Original entry on oeis.org
1, 0, 1, 2, 34, 877, 70400, 13131404, 6425063793, 7943767996608, 25443254098886314, 210703114432644635021, 4542702757904484984146944, 255390683442241619390980497544, 37530368819103589103825830619476133, 14431488687735756287625931644915850256384
Offset: 0
-
z = 16;
v[n_] := Table[Fibonacci[k], {k, 0, n - 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]]
Table[Simplify[Permanent[u[n]]], {n, 1, z}]
A384313
a(n) = pos(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (F(0), F(1), ..., F(n-1)), where F = A000045 (Fibonacci numbers), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.
Original entry on oeis.org
0, 0, 2, 9, 582, 27136, 7661772, 2797055478, 4374706319136, 11681281664592429, 112352959301265272414, 2147474541377915674682880, 133430162305143400794479937840, 18069411470335957872130103264497774, 7436752857750595469877425837627133763584
Offset: 1
The rows of M(4) are (0,1,1,2), (2,0,1,1), (1,2,0,1), (1,1,2,0); determinant(M(4)) = -16; permanent(M(4)) = 34, so neg(M(4)) = (-16 - 34)/2 = -25 and pos(M(4)) = (-16 + 34)/2 = 9.
-
z = 14;
v[n_] := Table[Fibonacci[k], {k, 0, n - 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]]
p = Table[Permanent[u[n]], {n, 1, z}] (* A384079 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A123744 *)
neg = (d - p)/2 (* A384080 *)
pos = (d + p)/2 (* A384313 *)
A384591
a(n) = permanent of the n X n circulant matrix with (row 1) = (F(1), F(2), ..., F(n)), where F = A000045 (Fibonacci numbers).
Original entry on oeis.org
1, 1, 2, 16, 265, 12552, 1431040, 426749895, 323397418338, 635720375415040, 3236089602490212389, 42921641465456435652532, 1485502760348227071906663424, 134453761950835461349077548216607, 31856917244136936392984483908703780290
Offset: 0
-
z = 14;
v[n_] := Table[Fibonacci[k], {k, 1, n}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]]
Table[Permanent[u[n]], {n, 1, z}]
Showing 1-3 of 3 results.