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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

%I #10 Mar 30 2012 18:37:32

%S 1,1,2,4,12,24,72,384,1104,2208,6624,35328,101568,28421376,67326336,

%T 366139392,983761152,1967522304,5902566912,31480356864,90506025984,

%U 25325947097088,59993690093568,326262418538496,876617757413376,248432976768114295652352,584740458214216890753024

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

%H Paul D. Hanna, <a href="/A200337/b200337.txt">Table of n, a(n) for n = 0..150</a>

%e Illustration of initial terms.

%e a(3) = a(0)*a(2) + a(2)*a(0) = 1*2 + 2*1 = 4.

%e 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.

%e a(5) = a(0)*a(4) + a(4)*a(0) = 1*12 + 12*1 = 24.

%e 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.

%e 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.

%o (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)))))}

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 16 2011

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Last modified March 28 04:05 EDT 2024. Contains 371235 sequences. (Running on oeis4.)