A290539 Determinant of circulant matrix of order eight with entries in the first row that are (-1)^(j-1) * Sum_{k>=0} (-1)^k*binomial(n,8*k+j-1), for j=1..8.
1, 0, 0, 0, 0, 0, 0, 0, -8489565952, -31872959692800, -932158289501356032, -4169183582652459909120, -5144394740685202662359040, -2505627397073121215653085184, -500556279165026162974748835840, 0, 20396260728315877590754520243175424
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..428
- Vladimir Shevelev, Combinatorial identities generated by difference analogs of hyperbolic and trigonometric functions of order n, arXiv:1706.01454 [math.CO], 2017.
- Wikipedia, Circulant matrix
Programs
-
Maple
seq(LinearAlgebra:-Determinant(Matrix(8,8,shape=Circulant[seq( (-1)^(j-1)*add((-1)^k*binomial(n,8*k+j-1),k=0..n/8),j=1..8)])), n=0..20); # Robert Israel, Aug 11 2017
-
Mathematica
ro[n_] := Table[(-1)^(j-1) Sum[(-1)^k*Binomial[n, 8k+j-1], {k, 0, n/8}], {j, 1, 8}]; M[n_] := Table[RotateRight[ro[n], m], {m, 0, 7}]; a[n_] := Det[M[n]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Aug 10 2018 *)
Comments