A200337 a(n+1) = Sum_{k=0..n, n XOR k <= n} a(k)*a(n XOR k) for n>=0 with a(0)=1.

1, 1, 2, 4, 12, 24, 72, 384, 1104, 2208, 6624, 35328, 101568, 28421376, 67326336, 366139392, 983761152, 1967522304, 5902566912, 31480356864, 90506025984, 25325947097088, 59993690093568, 326262418538496, 876617757413376, 248432976768114295652352, 584740458214216890753024

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..150

Example

Illustration of initial terms.
a(3) = a(0)*a(2) + a(2)*a(0) = 1*2 + 2*1 = 4.
a(4) = a(0)*a(3) + a(1)*a(2) + a(2)*a(1) + a(3)*a(0) = 1*4 + 1*2 + 2*1 + 4*1 = 12.
a(5) = a(0)*a(4) + a(4)*a(0) = 1*12 + 12*1 = 24.
a(6) = a(0)*a(5) + a(1)*a(4) + a(4)*a(1) + a(5)*a(0) = 1*24 + 1*12 + 12*1 + 24*1 = 72.
a(7) = a(0)*a(6) + a(2)*a(4) + a(3)*a(5) + a(4)*a(2) + a(5)*a(3) + a(6)*a(0) = 1*72 + 2*12 + 4*24 + 12*2 + 24*4 + 72*1 = 384.

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, if(bitxor(n-1, k)>=n, 0, a(k)*a(bitxor(n-1, k)))))}

Crossrefs

Sequence in context: A348642 A129643 A332644 * A367173 A367703 A320931

Adjacent sequences: A200334 A200335 A200336 * A200338 A200339 A200340

Keyword

nonn

Author

Paul D. Hanna, Nov 16 2011

Status

approved