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A099901
Shifts left and divides by 2 under the XOR BINOMIAL transform (A099902).
2
1, 2, 6, 14, 22, 46, 118, 206, 278, 558, 1654, 3790, 5910, 11310, 28790, 49358, 65814, 131630, 394870, 921294, 1447702, 3025966, 7762038, 13549774, 18284822, 36438574, 108004982, 247467726, 385881878, 738208814, 1879076982, 3221274830
OFFSET
0,2
COMMENTS
Equals the XOR BINOMIAL transform of A099902. Also, equals the leftmost column of the XOR difference triangle A099900, in which the central terms of the rows forms the powers of 2.
FORMULA
a(0)=1; a(n) = SumXOR_{k=0..n-1} (C(n-1-k+[k/2], [k/2])mod 2)*2^(k+1) for n>0. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A099902(n-i), where SumXOR is the analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).
PROG
(PARI) {a(n)=local(B); B=0; if(n==0, B=1, for(k=0, n-1, B=bitxor(B, binomial(n-1-k+k\2, k\2)%2*2^(k+1)))); B}
CROSSREFS
KEYWORD
eigen,nonn
AUTHOR
Paul D. Hanna, Oct 30 2004
STATUS
approved