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%I #21 Jan 26 2020 21:48:02
%S 1,3,7,11,23,59,103,139,279,827,1895,2955,5655,14395,24679,32907,
%T 65815,197435,460647,723851,1512983,3881019,6774887,9142411,18219287,
%U 54002491,123733863,192940939,369104407,939538491,1610637415,2147516555
%N Multiplies by 2 and shifts right under the XOR BINOMIAL transform (A099901).
%C Equals the XOR BINOMIAL transform of A099901. Also, equals the main diagonal of the XOR difference triangle A099900, in which the central terms of the rows form the powers of 2.
%C Bisection of A101624. - _Paul Barry_, May 10 2005
%H Robert Israel, <a href="/A099902/b099902.txt">Table of n, a(n) for n = 0..3290</a>
%F a(n) = SumXOR_{k=0..n} (binomial(n-k+floor(k/2), floor(k/2)) mod 2)*2^k for n >= 0.
%F a(n) = SumXOR_{i=0..n} (C(n, i) mod 2)*A099901(n-i), where SumXOR is the analog of summation under the binary XOR operation and C(i, j) mod 2 = A047999(i, j).
%F a(n) = Sum_{k=0..n} A047999(n-k+floor(k/2), floor(k/2)) * 2^k.
%F From _Paul Barry_, May 10 2005: (Start)
%F a(n) = Sum_{k=0..2n} (binomial(k, 2n-k) mod 2)*2^(2n-k);
%F a(n) = Sum_{k=0..n} (binomial(2n-k, k) mod 2)*2^k. (End)
%F a(n) = Sum_{k=0..2n} A106344(2n,k)*2^(2n-k). - _Philippe Deléham_, Dec 18 2008
%p a:= n -> add((binomial(n-k+floor(k/2),floor(k/2)) mod 2)*2^k, k=0..n):
%p map(a, [$0..100]); # _Robert Israel_, Jan 24 2016
%o (PARI) {a(n)=local(B);B=0;for(k=0,n,B=bitxor(B,binomial(n-k+k\2,k\2)%2*2^k));B}
%o (PARI) a(n)=sum(k=0,n,binomial(n-k+k\2,k\2)%2*2^k)
%Y Cf. A099884, A099900, A099901.
%K eigen,nonn
%O 0,2
%A _Paul D. Hanna_, Oct 30 2004
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