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 A112571 G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110637, which consists entirely of numbers 1 through 8. 1

%I

%S 1,1,3,-1,-2,6,0,-16,23,40,-140,13,591,-827,-1577,5887,-500,-27095,

%T 38922,77859,-295183,21310,1428714,-2069421,-4295099,16345171,-921876,

%U -81760620,118435457,253839799,-963510264,37372170,4936868645,-7119213992,-15717478733,59293735690

%N G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110637, which consists entirely of numbers 1 through 8.

%C A110637 is formed from every 4th 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 + 3*x^2 - x^3 - 2*x^4 + 6*x^5 - 16*x^7 + 23*x^8 +...

%e A(x)^2 = 1 + 2*x + 7*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + x^6 + 8*x^7 +...

%e A(x)^8 = 1 + 8*x + 52*x^2 + 216*x^3 + 754*x^4 + 2008*x^5 +...

%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=4,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))))^(1/2),n)}

%Y Cf. A110637, A083948.

%K sign

%O 0,3

%A _Paul D. Hanna_, Sep 14 2005

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Last modified January 26 03:23 EST 2022. Contains 350572 sequences. (Running on oeis4.)