This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 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)^(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 *) 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)