A117445 Periodic {0,-1,1,4,-1,4,-4,-4,1,1,-4,-4,4,-1,4,1,-1} (period 17).

0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1, -1, 0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1, -1, 0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1, -1, 0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1, -1, 0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4

Offset

0,4

Links

Table of n, a(n) for n=0..79.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1).

Formula

G.f.: (-1)*x*(1+x)*(1-x)^2*(1 -3*x^2 -3*x^3 -10*x^4 -6*x^5 -9*x^6 -6*x^7 -10*x^8 -3*x^9 -3*x^10 +x^12)/(1-x^17).

a(n) = (1/2)*Sum_{k=0..17} L(k*(k^2-n)/17), where L(j/p) is the Legendre symbol of j and p.

G.f.: (-x)*(1-x)*(1+x)*(1 -3*x^2 -3*x^3 -10*x^4 -6*x^5 -9*x^6 -6*x^7 -10*x^8 -3*x^9 -3*x^10 +x^12) )/(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10 +x^11 +x^12 +x^13 +x^14 +x^15 +x^16). - R. J. Mathar, Feb 23 2015

Mathematica

PadRight[{}, 60, {0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1, -1}] (* Harvey P. Dale, Sep 11 2012 *)
LinearRecurrence[{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, -1, 1, 4, -1, 4, -4, -4, 1, 1, -4, -4, 4, -1, 4, 1}, 80]
(* Ray Chandler, Jul 15 2015 *)

Crossrefs

Cf. A117444.

Sequence in context: A021711 A334487 A327304 * A145079 A196222 A035646

Adjacent sequences: A117442 A117443 A117444 * A117446 A117447 A117448

Keyword

easy,sign

Author

Paul Barry, Mar 16 2006

Status

approved