A084211 -id:A084211 - cp's OEIS frontend

A084212 G.f. A(x) defined by: A(x)^12 consists entirely of integer coefficients between 1 and 12 (A084067); A(x) is the unique power series solution with A(0)=1.

1, 1, -5, 37, -310, 2795, -26352, 256257, -2548875, 25793149, -264579518, 2743935678, -28716005918, 302812817148, -3213908529802, 34301475340630, -367873673112308, 3962187547336323

Offset: 0

Paul D. Hanna, May 20 2003

sign

Limit a(n)/a(n+1) --> r = -0.086930814654238 where A(r)=0.

Cf. A084067, A084202-A084211.

A084210 G.f. A(x) defined by: A(x)^10 consists entirely of integer coefficients between 1 and 10 (A083950); A(x) is the unique power series solution with A(0)=1.

Original entry on oeis.org

1, 1, -4, 25, -173, 1292, -10105, 81565, -673691, 5662878, -48263038, 415950272, -3617999891, 31714089336, -279828926113, 2483097203637, -22143011361045, 198317403322755

Offset: 0

Paul D. Hanna, May 20 2003

sign

Limit a(n)/a(n+1) --> r = -0.104430987675729 where A(r)=0.

Cf. A083950, A084202-A084209, A084211, A084212.

kmax = 20;
A[x_] = Sum[a[k] x^k, {k, 0, kmax}];
coes = CoefficientList[A[x]^10 + O[x]^(kmax + 1), x];
r = {a[0] -> 1, a[1] -> 1};
coes = coes /. r;
Do[r = Flatten @ Append[r, Reduce[1 <= coes[[k]] <= 10, a[k - 1], Integers] // ToRules];
coes = coes /. r, {k, 3, kmax + 1}];
Table[a[k], {k, 0, kmax}] /. r (* Jean-François Alcover, Jul 26 2018 *)

A110644 Every 11th term of A084066 such that the self-convolution 11th power is congruent modulo 121 to A084066, which consists entirely of numbers 1 through 11.

Original entry on oeis.org

1, 1, 7, 4, 9, 5, 5, 1, 5, 5, 11, 11, 9, 5, 11, 4, 8, 10, 10, 8, 10, 5, 11, 6, 1, 7, 1, 11, 5, 10, 1, 9, 4, 3, 9, 6, 8, 1, 6, 3, 4, 8, 2, 4, 4, 8, 10, 2, 4, 11, 1, 7, 11, 9, 11, 5, 2, 1, 4, 7, 9, 3, 2, 5, 8, 1, 8, 7, 4, 3, 2, 3, 5, 9, 1, 9, 5, 4, 1, 4, 6, 8, 5, 6, 9, 7, 4, 4, 5, 4, 6, 4, 10, 6, 6, 9, 9, 9, 4

Offset: 0

Robert G. Wilson v and Paul D. Hanna, Aug 08 2005

nonn

Congruent modulo 11 to A084211, where the self-convolution 11th power of A084211 equals A084066.

Cf. A084066, A111585, A084211.

{a(n)=local(p=11,A,C,X=x+x*O(x^(p*n)));if(n==0,1, A=sum(i=0,n-1,a(i)*x^(p*i))+p*x*((1-x^(p-1))/(1-X))/(1-X^p); for(k=1,p,C=polcoeff((A+k*x^(p*n))^(1/p),p*n); if(denominator(C)==1,return(k);break)))}

a(n) = A084066(11*n) for n>=0. G.f. satisfies: A(x^11) = G(x) - 11*x*((1-x^10)/(1-x))/(1-x^11), where G(x) is the g.f. of A084066. G.f. satisfies: A(x)^11 = A(x^11) + 11*x*((1-x^10)/(1-x))/(1-x^11) + 121*x^2*H(x) where H(x) is the g.f. of A111585.

cp's OEIS Frontend

A084212 G.f. A(x) defined by: A(x)^12 consists entirely of integer coefficients between 1 and 12 (A084067); A(x) is the unique power series solution with A(0)=1.

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A084210 G.f. A(x) defined by: A(x)^10 consists entirely of integer coefficients between 1 and 10 (A083950); A(x) is the unique power series solution with A(0)=1.

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A110644 Every 11th term of A084066 such that the self-convolution 11th power is congruent modulo 121 to A084066, which consists entirely of numbers 1 through 11.

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