login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181560 a(n+1) = a(n-1) + 2 a(n-2) - a(n-4) ; a(0)=1, a(n)=0 for 0 < n < 5; 0

%I

%S 1,0,0,0,0,-1,0,-1,-2,-1,-3,-5,-4,-9,-13,-14,-26,-36,-45,-75,-103,

%T -139,-217,-300,-420,-631,-881,-1254,-1843,-2596,-3720,-5401,-7658,

%U -10998,-15864,-22594,-32459,-46664,-66649,-95718,-137383,-196557,-282155

%N a(n+1) = a(n-1) + 2 a(n-2) - a(n-4) ; a(0)=1, a(n)=0 for 0 < n < 5;

%C a(n) is the constant term of the canonical representative (polynomial of degree < 5) of x^n (mod x^5-x^3-2*x^2+1), see example.

%F G.f.: sum( a(k) x^k, k=0...oo ) = (1 - x^2 - 2*x^3)/(1 - x^2 - 2*x^3 + x^5)

%e x^6 = x^4 + 2*x^3 - x (mod x^5 - x^3 - 2*x^2 + 1), and the l.h.s. has no constant term, so a(6) = 0.

%e x^14 = 14*x^4 + 26*x^3 + 22*x^2 - 9*x - 13 (mod x^5 - x^3 - 2*x^2 + 1), and the constant term on the r.h.s. is a(14) = -13.

%o (PARI) a(n) = polcoeff( lift( Mod( x, x^5-x^3-2*x^2+1)^n),0)

%K easy,sign

%O 0,9

%A _M. F. Hasler_, Nov 04 2010

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 29 04:54 EDT 2020. Contains 338066 sequences. (Running on oeis4.)