A112574 G.f. A(x) satisfies: A(x)^2 equals the g.f. of A110649, which consists entirely of numbers 1 through 12.
1, 3, 0, 2, 0, 3, -8, 30, -90, 290, -930, 3000, -9696, 31461, -102420, 334467, -1095510, 3598464, -11852026, 39136629, -129548493, 429817733, -1429178703, 4761992751, -15898024868, 53174651133, -178168302693, 597971203902, -2010093276240, 6767100270918
Offset: 0
Keywords
Examples
A(x) = 1 + 3*x + 2*x^3 + 3*x^5 - 8*x^6 + 30*x^7 - 90*x^8 +.. A(x)^2 = 1 + 6*x + 9*x^2 + 4*x^3 + 12*x^4 + 6*x^5 +... A(x)^4 = 1 + 12*x + 54*x^2 + 116*x^3 + 153*x^4 + 228*x^5 +.. A(x)^4 (mod 8) = 1 + 4*x + 6*x^2 + 4*x^3 + x^4 + 4*x^5 +... G(x) = 1 + 12*x + 6*x^2 + 4*x^3 + 9*x^4 + 12*x^5 + 4*x^6 +.. where G(x) is the g.f. of A084067.
Programs
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PARI
{a(n)=local(d=2,m=12,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)}
Formula
G.f. A(x) satisfies: A(x)^4 (mod 8) = g.f. of A084067.
Comments