A107089 -id:A107089 - cp's OEIS frontend

A223026 G.f. A(x) satisfies: A(x)^8 = A(x^2)^4 + 8*x.

1, 1, -3, 14, -76, 441, -2678, 16813, -108093, 707451, -4696017, 31530792, -213715953, 1460072247, -10042361784, 69473047716, -483046768116, 3373552141194, -23653214175084, 166422650191122, -1174621198245837, 8314055808436788, -58998774106863513

Offset: 0

Paul D. Hanna, Mar 11 2013

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The limit a(n+1)/a(n) seems to be near -7.46...

			G.f.: A(x) = 1 + x - 3*x^2 + 14*x^3 - 76*x^4 + 441*x^5 - 2678*x^6 +-...
where
A(x)^8 = 1 + 8*x + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +-...
A(x^2)^4 = 1 + 4*x^2 - 6*x^4 + 24*x^6 - 117*x^8 + 612*x^10 - 3426*x^12 +-...
A(x)^2 = 1 + 2*x - 5*x^2 + 22*x^3 - 115*x^4 + 646*x^5 - 3822*x^6 +-...

Paul D. Hanna, Table of n, a(n) for n = 0..300

Cf. A107086, A107089, A228711, A228712.

{a(n)=local(A=1+x); for(i=1, #binary(n), A=(subst(A, x, x^2)^4+8*x+x*O(x^n))^(1/8)); polcoeff(A, n, x)}
for(n=0, 20, print1(a(n), ", "))

Self-convolution yields A228711.

A107090 G.f. A(x) satisfies: A(x)^3 = A(x^3) + 9*x.

Original entry on oeis.org

1, 3, -9, 46, -276, 1827, -12838, 93885, -706878, 5440856, -42608139, 338345586, -2717685006, 22039352340, -180191062062, 1483568585389, -12289222187157, 102343255814052, -856335797389803, 7195400130323322, -60687964204960104, 513600833339124915

Offset: 0

Paul D. Hanna, May 11 2005

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Self-convolution cube of A107089. Self-convolution cube yields A107091.

			A(x)^3 = 1 + 9*x + 3*x^3 - 9*x^6 + 46*x^9 - 276*x^12 + 1827*x^15 -+...
A(x^3) = 1 + 3*x^3 - 9*x^6 + 46*x^9 - 276*x^12 + 1827*x^15 -+...

Cf. A107089, A107091.

{a(n)=local(A=1+x);for(i=1,n,A=(subst(A,x,x^3)+9*x+x*O(x^n))^(1/3)); polcoeff(A,n,x)}

A107091 G.f. A(x) satisfies: A(x) = A(x^3)^(1/3) + 9*x.

Original entry on oeis.org

1, 9, 0, 3, 0, 0, -9, 0, 0, 46, 0, 0, -276, 0, 0, 1827, 0, 0, -12838, 0, 0, 93885, 0, 0, -706878, 0, 0, 5440856, 0, 0, -42608139, 0, 0, 338345586, 0, 0, -2717685006, 0, 0, 22039352340, 0, 0, -180191062062, 0, 0, 1483568585389, 0, 0, -12289222187157, 0, 0, 102343255814052, 0, 0, -856335797389803, 0, 0

Offset: 0

Paul D. Hanna, May 11 2005

sign

Self-convolution 9th power of A107089. Self-convolution cube of A107090.

			A(x) = 1 + 9*x + 3*x^3 - 9*x^6 + 46*x^9 - 276*x^12 + 1827*x^15 -+...
A(x^3)^(1/3) = 1 + 3*x^3 - 9*x^6 + 46*x^9 - 276*x^12 + 1827*x^15 -+...

Cf. A107089, A107090.

{a(n)=local(A=1+x);for(i=1,n,A=(subst(A^3,x,x^3)+9*x+x*O(x^n))^(1/9)); polcoeff(A^9,n,x)}

cp's OEIS Frontend

A223026 G.f. A(x) satisfies: A(x)^8 = A(x^2)^4 + 8*x.

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A107090 G.f. A(x) satisfies: A(x)^3 = A(x^3) + 9*x.

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A107091 G.f. A(x) satisfies: A(x) = A(x^3)^(1/3) + 9*x.

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PARI