|
%I #6 Mar 10 2015 02:13:02
%S 1,1,1,1,-1,2,0,1,-2,5,-5,4,-6,18,-30,35,-43,84,-167,261,-352,545,
%T -1010,1790,-2783,4207,-7025,12464,-21071,33567,-54154,92317,-159366,
%U 266150,-435285,725260,-1239404,2112351,-3535532,5894852,-9964767,17008752,-28880694,48645873
%N G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110630, which consists entirely of numbers 1 through 4.
%C A110630 is formed from every 2nd term of A083954, which also consists entirely of numbers 1 through 4.
%F G.f. A(x) satisfies: A(x)^4 (mod 8) = g.f. of A083954.
%e A(x) = 1 + x + x^2 + x^3 - x^4 + 2*x^5 + x^7 - 2*x^8 + 5*x^9 +...
%e A(x)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + x^4 + 4*x^5 + 3*x^6 +...
%e A(x)^4 = 1 + 4*x + 10*x^2 + 20*x^3 + 27*x^4 + 36*x^5 +...
%e A(x)^4 (mod 8) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 +...
%e G(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 3*x^4 + 4*x^5 + 4*x^6 +...
%e where G(x) is the g.f. of A083954.
%o (PARI) {a(n)=local(d=2,m=4,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break))); polcoeff(Ser(vector(n+1,i,polcoeff(A,d*(i-1))))^(1/2),n)}
%Y Cf. A110630, A083954.
%K sign
%O 0,6
%A _Paul D. Hanna_, Sep 14 2005
|
