|
%I #6 Mar 10 2015 02:12:41
%S 1,1,-1,3,-6,18,-52,156,-481,1512,-4828,15621,-51081,168537,-560309,
%T 1874975,-6309964,21341241,-72497698,247247463,-846187023,2905210526,
%U -10003144986,34532780087,-119499263663,414431066955,-1440182574644,5014115406096
%N G.f. A(x) satisfies: A(x)^4 equals the g.f. of A110638, which consists entirely of numbers 1 through 8.
%C A110638 is formed from every 2nd term of A083948, which also consists entirely of numbers 1 through 8.
%F G.f. A(x) satisfies: A(x)^8 (mod 16) = g.f. of A083948.
%e A(x) = 1 + x - x^2 + 3*x^3 - 6*x^4 + 18*x^5 - 52*x^6 + 156*x^7 +...
%e A(x)^4 = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
%e A(x)^8 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 + 116*x^6 +...
%e A(x)^8 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
%e G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
%e where G(x) is the g.f. of A083948.
%o (PARI) {a(n)=local(d=2,m=8,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))))^(1/4),n)}
%Y Cf. A110638, A083948, A112571.
%K sign
%O 0,4
%A _Paul D. Hanna_, Sep 14 2005
|
