OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..226
Eric Weisstein's World of Mathematics, Circulant Matrix.
FORMULA
a(n) = (-1)^(n-1)*n^(n-2)*(n+1)*(n-1)*((n+1)^n-(n-1)^n)/(6*2^n). [Missouri State University Problem-Solving Group (MSUPSG(AT)MissouriState.edu), May 03 2010]
EXAMPLE
a(2) = - 1 because of the determinant -1 =
| 0, 1 |
| 1, 0 |.
a(4) = -1360 = determinant
|0,1,3,6|
|6,0,1,3|
|3,6,0,1|
|1,3,6,0|.
MAPLE
f:= proc(n) uses LinearAlgebra; local i;
Determinant(Matrix(n, shape=Circulant[[seq(i*(i+1)/2, i=0..n-1)]]))
end proc:
map(f, [$1..30]); # Robert Israel, Jan 25 2023
MATHEMATICA
r[n_] := r[n] = Table[k(k+1)/2, {k, 0, n-1}];
M[n_] := Table[RotateRight[r[n], m-1], {m, 1, n}];
a[n_] := Det[M[n]];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 11 2023 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Jonathan Vos Post, May 20 2006
EXTENSIONS
More terms from Alois P. Heinz, Mar 16 2017
STATUS
approved