A110638 -id:A110638 - cp's OEIS frontend

A112572 G.f. A(x) satisfies: A(x)^4 equals the g.f. of A110638, which consists entirely of numbers 1 through 8.

1, 1, -1, 3, -6, 18, -52, 156, -481, 1512, -4828, 15621, -51081, 168537, -560309, 1874975, -6309964, 21341241, -72497698, 247247463, -846187023, 2905210526, -10003144986, 34532780087, -119499263663, 414431066955, -1440182574644, 5014115406096

Offset: 0

Paul D. Hanna, Sep 14 2005

sign

A110638 is formed from every 2nd term of A083948, which also consists entirely of numbers 1 through 8.

			A(x) = 1 + x - x^2 + 3*x^3 - 6*x^4 + 18*x^5 - 52*x^6 + 156*x^7 +...
A(x)^4 = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +...
A(x)^8 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 + 116*x^6 +...
A(x)^8 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 + 8*x^7 +...
where G(x) is the g.f. of A083948.

Cf. A110638, A083948, A112571.

{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)}

G.f. A(x) satisfies: A(x)^8 (mod 16) = g.f. of A083948.

A110637 Every 4th term of A083948 where the self-convolution 4th power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.

Original entry on oeis.org

1, 2, 7, 4, 3, 2, 1, 8, 6, 6, 6, 4, 4, 2, 8, 8, 7, 6, 8, 6, 8, 6, 7, 8, 3, 4, 3, 6, 3, 8, 1, 4, 4, 8, 3, 6, 6, 2, 5, 8, 1, 4, 6, 4, 6, 6, 1, 8, 1, 6, 5, 8, 4, 4, 8, 4, 5, 8, 5, 2, 4, 8, 6, 4, 5, 2, 8, 8, 7, 4, 6, 4, 5, 8, 6, 8, 6, 4, 5, 4, 8, 4, 4, 4, 7, 8, 4, 2, 1, 8, 3, 4, 7, 2, 7, 8, 4, 6, 6, 4, 8, 6, 7, 6, 4

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 30 2005

nonn

			A(x) = 1 + 2*x + 7*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + x^6 +...
A(x)^4 = 1 + 8*x + 52*x^2 + 216*x^3 + 754*x^4 + 2008*x^5 +...
A(x)^4 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +...
G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 +...
where G(x) is the g.f. of A083948.

Cf. A083948, A110636, A110638.

{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(A,d*n)}

cp's OEIS Frontend

A112572 G.f. A(x) satisfies: A(x)^4 equals the g.f. of A110638, which consists entirely of numbers 1 through 8.

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