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URL: https://oeis.org/A227526

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A227526
G.f.: Sum_{n>=0} x^n * (1+x)^A003188(n), where A003188(n) = n XOR [n/2] is the Gray code for n.
2
1, 1, 2, 4, 6, 9, 23, 47, 65, 70, 111, 323, 902, 2064, 3997, 6697, 9638, 11664, 11804, 11436, 18903, 61053, 209236, 623648, 1610326, 3685365, 7673031, 14926689, 27784642, 50202979, 88022528, 147757232, 232939294, 338735927, 448199945, 534600063, 571408283, 546281026, 475461610
OFFSET
0,3
COMMENTS
A(-1/2) = Sum_{n>=0} (-1)^n / 2^(n + A003188(n)) = 0.75073331594540770872470210...
LINKS
FORMULA
a(n) = Sum_{k=0..n} binomial(A003188(k), n-k), where A003188(k) = k XOR [k/2].
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 + 9*x^5 + 23*x^6 + 47*x^7 + 65*x^8 +...
where
A(x) = 1 + x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^2 + x^4*(1+x)^6 + x^5*(1+x)^7 + x^6*(1+x)^5 + x^7*(1+x)^4 + x^8*(1+x)^12 + x^9*(1+x)^13 + x^10*(1+x)^15 + x^11*(1+x)^14 + x^12*(1+x)^10 + x^13*(1+x)^11 + x^14*(1+x)^9 + x^15*(1+x)^8 +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+x+x*O(x^n))^bitxor(m, m\2)), n)}
for(n=0, 64, print1(a(n), ", "))
(PARI) {a(n) = sum(k=0, n, binomial(bitxor(k, k\2), n-k))}
for(n=0, 64, print1(a(n), ", "))
CROSSREFS
Sequence in context: A049912 A268868 A271927 * A093081 A242521 A338298
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 14 2013
STATUS
approved