A384080
a(n) = neg(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 neg(M(n)) is the negative part of the determinant of M(n); see A380661.
Original entry on oeis.org
0, -1, 0, -25, -295, -43264, -5469632, -3628008315, -3569061677472, -13761972434293885, -98350155131379362607, -2395228216526569309464064, -121960521137098218596500559704, -19460957348767631231695727354978359, -6994735829985160817748505807288716492800
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, with alternating signs *)
neg = (d - p)/2 (* A384080 *)
pos = (d + p)/2 (* A384313 *)
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 *)
A384594
a(n) = permanent of the n X n circulant matrix with (row 1) = (F(2), F(3), ..., F(n+1)), where F = A000045 (Fibonacci numbers).
Original entry on oeis.org
1, 1, 5, 54, 1689, 126379, 24431584, 11866142075, 14794067672433, 47379803431959808, 392931276153375379253, 8465684295123427342668831, 475511457476096446534113500160, 69772090836124641206618567332180231, 26784700757594331263875776507073783052317
Offset: 0
-
z = 14;
v[n_] := Table[Fibonacci[k], {k, 2, n + 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]];
Table[Permanent[u[n]], {n, 1, z}]
Showing 1-3 of 3 results.