%I #28 May 03 2021 12:19:03
%S 0,1,1,5,1,21,17,69,1,277,273,1349,257,5141,4113,16453,1,65813,65809,
%T 329029,65793,1381397,1118225,4538437,65537,18088213,17826065,
%U 88081733,16777473,335549461,268439569,1073758277,1,4295033109,4295033105
%N A bisection of the Stern-Jacobsthal numbers.
%H Ivan Panchenko, <a href="/A101625/b101625.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} (binomial(2n-k, k-1) mod 2)2^(k-1);
%F a(n) = A101624(2n+1).
%F a(0)=0, a(1)=1, a(n) = a(n-1) XOR (a(n-2)*4), where XOR is the bitwise exclusive-OR operator. - _Alex Ratushnyak_, May 06 2012
%F a(n+1) = Sum_{k=0..n} A106344(n,k)*4^(n-k). - _Philippe Deléham_, May 27 2012
%o (Python)
%o prpr = 0
%o prev = 1
%o for i in range(99):
%o current = (prev)^(prpr*4)
%o print(prpr, end=',')
%o prpr = prev
%o prev = current
%o # _Alex Ratushnyak_, May 06 2012
%Y Cf. A002450.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Dec 10 2004