

A290535


Determinant of circulant matrix of order 6 with entries in the first row (1)^(j1)*Sum_{k>=0} (1)^k*binomial(n, 6*k + j  1), j=1..6.


2



1, 0, 0, 0, 0, 0, 104284, 783050688, 329029322076, 43271152876224, 2175830808446736, 0, 5427970251634650916, 307609249050423946080, 8866068073884849492756, 137518739026000524646272, 896278292839676023110288, 0, 2518571790589921864549097500
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OFFSET

0,7


COMMENTS

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


LINKS

Table of n, a(n) for n=0..18.
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


MATHEMATICA

ro[n_] := Table[(1)^(j1) Sum[(1)^k Binomial[n, 6k+j1], {k, 0, n/6}], {j, 1, 6}];
M[n_] := Table[RotateRight[ro[n], m], {m, 0, 5}];
a[n_] := Det[M[n]];
Table[a[n], {n, 0, 18}] (* JeanFrançois Alcover, Aug 10 2018 *)


CROSSREFS

Cf. A290285, A290286.
Sequence in context: A076761 A236007 A129241 * A253709 A235005 A231143
Adjacent sequences: A290532 A290533 A290534 * A290536 A290537 A290538


KEYWORD

sign


AUTHOR

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


STATUS

approved



