The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193620 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n * A(x)^A026250(n). 1
 1, 1, 4, 22, 132, 875, 6127, 44580, 333748, 2553956, 19887080, 157066758, 1255181598, 10130663492, 82461801961, 676165571433, 5580011570160, 46309238031602, 386256008451734, 3236134144224075, 27222318068596831, 229828039356161276, 1946773238298955438 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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). LINKS FORMULA G.f. satisfies: A(x) = 1 + Sum_{n>=1} A(x)^n * x^A026250(n). EXAMPLE 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,...]. PROG (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)} CROSSREFS Cf. A026250, A193621. Sequence in context: A007195 A356283 A292838 * A321275 A274745 A197657 Adjacent sequences: A193617 A193618 A193619 * A193621 A193622 A193623 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 01 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 22 01:15 EDT 2023. Contains 361413 sequences. (Running on oeis4.)