A228835 G.f. satisfies: A(x) = x + A(x^2 + A(x^3 + A(x^4 + A(x^5 +...)))).

1, 1, 1, 2, 3, 6, 10, 20, 38, 75, 145, 288, 571, 1147, 2304, 4652, 9413, 19133, 38999, 79753, 163489, 335996, 692028, 1428351, 2953637, 6118456, 12694486, 26377235, 54881902, 114333228, 238460819, 497883758, 1040572232, 2176812874, 4557723208, 9550565627, 20028241000, 42030974050

Offset

1,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..380

Example

G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 6*x^6 + 10*x^7 + 20*x^8 +...
where A(x) = x + A(x^2 + B(x));
B(x) = A(x^3 + C(x)) = x^3 + x^4 + x^5 + 2*x^6 + 3*x^7 + 5*x^8 + 8*x^9 + 13*x^10 + 21*x^11 + 36*x^12 +...;
C(x) = A(x^4 + D(x)) = x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + 2*x^10 + 3*x^11 + 5*x^12 + 7*x^13 + 10*x^14 +...;
D(x) = A(x^5 + E(x)) = x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + 2*x^12 + 3*x^13 + 5*x^14 + 7*x^15 + 10*x^16 +...;
E(x) = A(x^6 + F(x)) = x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + 2*x^14 + 3*x^15 + 5*x^16 + 7*x^17 + 10*x^18 +...; ...

Prog

(PARI) {a(n)=local(G=x+x^2, A=G); for(i=1, n+1, A=G; G=x^(n+1); for(m=0, n, G=x^(n-m+1)+subst(A, x, G+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))

Crossrefs

Sequence in context: A331693 A123423 A005195 * A052843 A120707 A047111

Adjacent sequences: A228832 A228833 A228834 * A228836 A228837 A228838

Keyword

nonn

Author

Paul D. Hanna, Sep 05 2013

Status

approved