A384076
a(n) = pos(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (1,3,5,7, ..., 2n - 1), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.
Original entry on oeis.org
1, 1, 153, 2668, 250200, 19423560, 2515242520, 404114856640, 84196030473216, 21703670967664000, 6808856052755927808, 2552126898198385479168, 1126590812208410998119424, 578462173661889165983466496, 341831898528862885226121600000
Offset: 1
The rows of M(4) are (1,3,5,7), (7,1,3,5), (5,7,1,3), (3,5,7,1); determinant(M(4)) = -4716; permanent(M(4)) = 2668, so neg(M(4)) = (-2048 - 7384)/2 = -4716 and pos(M(4)) = (-2048 + 7384)/2 = 2668.
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z = 19;
v[n_] := Table[2 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}] (* A384074 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A193678,, with alternating signs *)
neg = (d - p)/2 (* A384075 *)
pos = (d + p)/2 (* A384076 *)
A384078
a(n) = pos(M(n)), where M(n) is the n X n left circulant matrix with (row 1) = (1,3,5,7, ..., 2n - 1), and pos(M(n)) is the positive part of the determinant of M(n); see A380661.
Original entry on oeis.org
1, 1, 45, 4716, 250200, 19423560, 2462535768, 406262340288, 84196030473216, 21703670967664000, 6808563893605222144, 2552145158372103507456, 1126590812208410998119424, 578462173661889165983466496, 341831891354409385226121600000
Offset: 1
The rows of M(4) are (1,3,5,7), (3,5,7,1), (5,7,1,3), (7,1,3,5); determinant(M(4)) = 2048; permanent(M(4)) = 7384, so neg(M(4)) = (7384 - 2048)/2 = -2668 and pos(M(4)) = (7384+2048)/2 = 4716.
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z = 15;
v[n_] := Table[2 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}] (* A384074 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A193678 up to signs *)
neg = (d - p)/2 (* A384077 *)
pos = (d + p)/2 (* A384078 *)
A384074
a(n) = permanent of the n X n circulant matrix with (row 1) = (1, 3, 5, 7, ..., 2n - 1).
Original entry on oeis.org
1, 10, 198, 7384, 450400, 40340112, 4977778288, 810377196928, 168292881301248, 43412461935328000, 13617419946361149952, 5104272056570488986624, 2253180383840385394370560, 1156924438353338246938200064, 683663789883272270452243200000
Offset: 1
-
z = 16; v[n_] := Table[2 k + 1, {k, 0, n - 1}];
u[n_] := Table[RotateRight[#, k - 1], {k, 1, Length[#]}] &[v[n]];
Table[Simplify[Permanent[u[n]]], {n, 1, z}]
A384075
a(n) = neg(M(n)), where M(n) is the n X n circulant matrix with (row 1) = (1,3,5,7, ..., 2n - 1), and neg(M(n)) is the negative part of the determinant of M(n); see A380661.
Original entry on oeis.org
0, -9, -45, -4716, -200200, -20916552, -2462535768, -406262340288, -84096850828032, -21708790967664000, -6808563893605222144, -2552145158372103507456, -1126589571631974396251136, -578462264691449080954733568, -341831891354409385226121600000
Offset: 1
The rows of M(4) are (1,3,5,7), (7,1,3,5), (5,7,1,3), (3,5,7,1); determinant(M(4)) = -4716; permanent(M(4)) = 2668, so neg(M(4)) = (-2048 - 7384)/2 = -4716 and pos(M(4)) = (-2048 + 7384)/2 = 2668.
-
z = 19;
v[n_] := Table[2 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}] (* A384074 *)
d = Table[Simplify[Det[u[n]]], {n, 1, z}] (* A193678, with alternating signs *)
neg = (d - p)/2 (* A384075 *)
pos = (d + p)/2 (* A384076 *)
Showing 1-4 of 4 results.