A193620 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n * A(x)^A026250(n).

1, 1, 4, 22, 132, 875, 6127, 44580, 333748, 2553956, 19887080, 157066758, 1255181598, 10130663492, 82461801961, 676165571433, 5580011570160, 46309238031602, 386256008451734, 3236134144224075, 27222318068596831, 229828039356161276, 1946773238298955438

Offset: 0

Author

Paul D. Hanna, Sep 01 2011

Keywords

• nonn

Comments

Sequence A026250 is a self-inverse permutation of the natural numbers where

A026250([k*sqrt(2)]) = [k*(2+sqrt(2))] and

A026250([k*(2+sqrt(2))]) = [k*sqrt(2)] for k>=1, and [x] = floor(x).

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 132*x^4 + 875*x^5 + 6127*x^6 +...
where A(x) = 1 + x*A(x)^3 + x^2*A(x)^6 + x^3*A(x) + x^4*A(x)^10 + x^5*A(x)^13 + x^6*A(x)^2 + x^7*A(x)^17 + x^8*A(x)^20 + x^9*A(x)^23 + x^10*A(x)^4 +...
which also equals: A(x) = 1 + A(x)*x^3 + A(x)^2*x^6 + A(x)^3*x + A(x)^4*x^10 + A(x)^5*x^13 + A(x)^6*x^2 + A(x)^7*x^17 + A(x)^8*x^20 + A(x)^9*x^23 + A(x)^10*x^4 +...
In the above series, the exponents begin:
A026250 = [3,6,1,10,13,2,17,20,23,4,27,30,5,34,37,40,7,44,47,8,51,...].
		

Crossrefs

Cf. A026250, A193621.

Programs

PARI

{a(n)=local(A=1+x,s=sqrt(2),t=2+sqrt(2));for(i=1,n,A=1+sum(m=1,n, x^floor(m*s)*(A+x*O(x^n))^floor(m*t) + x^floor(m*t)*(A+x*O(x^n))^floor(m*s) )); polcoeff(A, n)}

Formula

G.f. satisfies: A(x) = 1 + Sum_{n>=1} A(x)^n * x^A026250(n).