A224272 G.f. satisfies: A(x) = (A(x^2) + x)^2.

1, 2, 5, 4, 14, 10, 28, 8, 69, 28, 116, 20, 252, 56, 340, 16, 726, 138, 916, 56, 1982, 232, 2120, 40, 4844, 504, 4860, 112, 11320, 680, 9520, 32, 24525, 1452, 19508, 276, 51636, 1832, 34636, 112, 104388, 3964, 67480, 464, 203676, 4240, 110288, 80, 388732, 9688, 206908, 1008

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1024

Formula

a(m*2^n-1) = a(m-1)*2^n for n>=0, m>=1:

a(2^n-1) = 2^n, a(3*2^n-1) = 5*2^n, a(5*2^n-1) = 14*2^n, for n>=0.

a(m) is odd iff m = 2*4^n (n>=0) or m=0.

a(2*4^n) == 5 (mod 8) for n>=0.

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 4*x^3 + 14*x^4 + 10*x^5 + 28*x^6 + 8*x^7 + 69*x^8 + 28*x^9 + 116*x^10 + 20*x^11 + 252*x^12 +...
where
A(x)^(1/2) = 1 + x + 2*x^2 + 5*x^4 + 4*x^6 + 14*x^8 + 10*x^10 + 28*x^12 + 116*x^20 + 20*x^22 + 252*x^24 +...
A(x)^2 = 1 + 4*x + 14*x^2 + 28*x^3 + 69*x^4 + 116*x^5 + 252*x^6 + 340*x^7 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, #binary(n+1), A=(subst(A, x, x^2) + x +x*O(x^n))^2); polcoeff(A, n, x)}
for(n=0, 64, print1(a(n), ", "))

Crossrefs

Sequence in context: A252668 A225046 A079053 * A189942 A251554 A002518

Adjacent sequences: A224269 A224270 A224271 * A224273 A224274 A224275

Keyword

nonn

Author

Paul D. Hanna, Apr 02 2013

Status

approved