login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n+8)+34*a(n+4)+a(n)=0 with a(0)-a(7) as shown.
2

%I #18 Jun 24 2024 08:54:25

%S 1,5,12,12,-29,-169,-408,-408,985,5741,13860,13860,-33461,-195025,

%T -470832,-470832,1136689,6625109,15994428,15994428,-38613965,

%U -225058681,-543339720,-543339720,1311738121,7645370045,18457556052,18457556052,-44560482149

%N a(n+8)+34*a(n+4)+a(n)=0 with a(0)-a(7) as shown.

%H Colin Barker, <a href="/A259860/b259860.txt">Table of n, a(n) for n = 0..1000</a>

%H J. Riordan, <a href="http://www.jstor.org/stable/2005477">The distribution of crossings of chords joining pairs of 2n points on a circle</a>, Math. Comp., 29 (1975), 215-222.

%H J. Riordan, <a href="/A003480/a003480.pdf">The distribution of crossings of chords joining pairs of 2n points on a circle</a>, Math. Comp., 29 (1975), 215-222. [Annotated scanned copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-8,4,-1).

%F G.f.: (x+1) / (x^4-4*x^3+8*x^2-4*x+1). - _Colin Barker_, Jul 09 2015

%p A259860 := proc(n)

%p if n <= 7 then

%p op(n+1,[1, 5, 12, 12, -29, -169, -408, -408, 985, 5741, 13860, 13860]) ;

%p else

%p -34*procname(n-4)-procname(n-8) ;

%p fi ;

%p end proc: # _R. J. Mathar_, Jun 24 2024

%t LinearRecurrence[{4,-8,4,-1},{1,5,12,12},40] (* _Harvey P. Dale_, Mar 14 2016 *)

%o (PARI) Vec((x+1)/(x^4-4*x^3+8*x^2-4*x+1) + O(x^50)) \\ _Colin Barker_, Jul 09 2015

%Y Cf. A259861.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 08 2015