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.
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
Offset: 0
Keywords
Examples
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 +...
Links
- Paul D. Hanna, Table of n, a(n) for n = 0..1024
Programs
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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), ", "))
Comments