|
| |
|
|
A227527
|
|
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, 0, -2, 2, -5, 9, -3, -13, 14, 35, -149, 300, -450, 673, -1151, 1856, -2366, 2424, -3192, 9319, -32687, 96858, -238410, 508290, -998065, 1925065, -3750685, 7162328, -12635545, 19437562, -24482990, 22154946, -6283107, -25823457, 69598597, -113006459, 140737910, -137007218, 67953174
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
A(1/2) = Sum_{n>=0} 1/2^(n + A003188(n)) = 1.3146990537656455533266364007421...
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(A003188(k), n-k), where A003188(k) = k XOR [k/2].
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 + x - 2*x^3 + 2*x^4 - 5*x^5 + 9*x^6 - 3*x^7 - 13*x^8 + 14*x^9 +...
where A(x) = A(1-x) equals the series:
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, (-1)^(n-k)*binomial(bitxor(k, k\2), n-k))}
for(n=0, 64, print1(a(n), ", "))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
