

A290539


Determinant of circulant matrix of order eight with entries in the first row that are (1)^(j1) * Sum_{k>=0} (1)^k*binomial(n,8*k+j1), for j=1..8.


2



1, 0, 0, 0, 0, 0, 0, 0, 8489565952, 31872959692800, 932158289501356032, 4169183582652459909120, 5144394740685202662359040, 2505627397073121215653085184, 500556279165026162974748835840, 0, 20396260728315877590754520243175424
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,9


COMMENTS

a(n) = 0 for n == 7 (mod 8).


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


MAPLE

seq(LinearAlgebra:Determinant(Matrix(8, 8, shape=Circulant[seq(
(1)^(j1)*add((1)^k*binomial(n, 8*k+j1), k=0..n/8), j=1..8)])), n=0..20); # Robert Israel, Aug 11 2017


MATHEMATICA

ro[n_] := Table[(1)^(j1) Sum[(1)^k*Binomial[n, 8k+j1], {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}] (* JeanFrançois Alcover, Aug 10 2018 *)


CROSSREFS

Cf. A290285, A290286, A290535, A290540.
Sequence in context: A250865 A108880 A204500 * A017003 A017075 A017267
Adjacent sequences: A290536 A290537 A290538 * A290540 A290541 A290542


KEYWORD

sign


AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Aug 05 2017


STATUS

approved



