A226279 - OEIS

%I #29 Dec 23 2023 08:44:32

%S 0,-1,0,-1,2,1,2,1,4,3,4,3,6,5,6,5,8,7,8,7,10,9,10,9,12,11,12,11,14,

%T 13,14,13,16,15,16,15,18,17,18,17,20,19,20,19,22,21,22,21,24,23,24,23,

%U 26,25,26,25,28,27,28,27,30,29,30,29

%N a(4n) = a(4n+2) = 2*n , a(4n+1) = a(4n+3) = 2*n-1.

%C a(n)=c(n) in A214297(n).

%C In A214297 d(n)=-1,1,1,3,1,3,3,... = mix (-A186422(2n) , A186422(2n+1)).

%C A214297 is the (reduced) numerator of 1/4 - 1/A061038(n).

%C (i.e. (1/4 -(1/0, 1/4, 1, 1/36, 1/16,...)) = -1/0, 0/1, -3/4, 2/9, 3/16,... )

%C 1/0 is a convention.

%C n^2=(a(n+1)+d(n+1))^2 are the denominators.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).

%F a(0) = a(2)=0, a(1)=a(3)=-1, a(4)=2.

%F a(n) = a(n-4) + 2, n > 3.

%F a(n) = a(n-1) + a(n-4) - a(n-5), n > 4.

%F A214297(n) = a(n+1) * d(n+1).

%F G.f.: x*(3*x^3-x^2+x-1) / ((x-1)^2*(x+1)*(x^2+1)). - _Colin Barker_, Sep 22 2013

%t Table[{0, -1} + 2*Floor[n/2], {n, 0, 31}] // Flatten (* _Jean-François Alcover_, Jun 03 2013 *)

%o (PARI) a(n)=n\4*2-n%2 \\ _Charles R Greathouse IV_, Sep 15 2013

%Y Cf. A134967, A162330, A103889, A000290.

%K sign,easy

%O 0,5

%A _Paul Curtz_, Jun 02 2013