A290535 - OEIS

%I #26 Aug 10 2018 02:36:12

%S 1,0,0,0,0,0,-104284,-783050688,-329029322076,-43271152876224,

%T -2175830808446736,0,5427970251634650916,307609249050423946080,

%U 8866068073884849492756,137518739026000524646272,896278292839676023110288,0,-2518571790589921864549097500

%N Determinant of circulant matrix of order 6 with entries in the first row (-1)^(j-1)*Sum_{k>=0} (-1)^k*binomial(n, 6*k + j - 1), j=1..6.

%C a(n) = 0 for n == 5 (mod 6).

%H Vladimir Shevelev, <a href="https://arxiv.org/abs/1706.01454">Combinatorial identities generated by difference analogs of hyperbolic and trigonometric functions of order n</a>, arXiv:1706.01454 [math.CO], 2017.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>

%t ro[n_] := Table[(-1)^(j-1) Sum[(-1)^k Binomial[n, 6k+j-1], {k, 0, n/6}], {j, 1, 6}];

%t M[n_] := Table[RotateRight[ro[n], m], {m, 0, 5}];

%t a[n_] := Det[M[n]];

%t Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Aug 10 2018 *)

%Y Cf. A290285, A290286.

%K sign

%O 0,7

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Aug 05 2017