A163137 G.f. A(x) equals an infinite symmetric composition of functions x+x^n, n=2,3,4,...

1, 2, 4, 13, 39, 113, 359, 1161, 3708, 11961, 38903, 126885, 415509, 1365935, 4501009, 14856863, 49115474, 162590020, 538828790, 1787431873, 5934532485, 19718347615, 65559507987, 218095336290, 725890070743, 2417022095921

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Formula

G.f.: A(x) = x+x^2 o x+x^3 o...o x+x^n o...o (x) o...o x+x^n o...o x+x^3 o x+x^2.

Example

G.f.: A(x) = x + 2*x^2 + 4*x^3 + 13*x^4 + 39*x^5 + 113*x^6 +...
G.f. A(x) equals the limit of symmetric compositions starting with:
(1) x+x^2 o x+x^2 = x + 2*x^2 + 2*x^3 + x^4 ;
(2) x+x^2 o x+x^3 o x+x^3 o x+x^2 = x + 2*x^2 + 4*x^3 + 11*x^4 +...;
(3) x+x^2 o x+x^3 o x+x^4 o x+x^4 o x+x^3 o x+x^2 = x + 2*x^2 + 4*x^3 + 13*x^4 +...

Prog

(PARI) {a(n)=local(F=x); if(n<1, 0, for(k=2, n, F=subst(subst(x+x^(n-k+2), x, F), x, x+x^(n-k+2)+x*O(x^n)); ); return(polcoeff(F, n)))}

Crossrefs

Cf. A163136, A163135.

Sequence in context: A174604 A148253 A148254 * A093630 A033091 A282741

Adjacent sequences: A163134 A163135 A163136 * A163138 A163139 A163140

Keyword

nonn

Author

Paul D. Hanna, Aug 16 2009

Status

approved