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A099899 Multiplies by 4 and shifts right under the XOR BINOMIAL transform (A099898). 2
1, 5, 21, 69, 277, 1349, 5141, 16453, 65813, 329029, 1381397, 4538437, 18088213, 88081733, 335549461, 1073758277, 4295033109, 21475165509, 90195694613, 296357281861, 1189724029205, 5793998964037, 22080762418197, 70666170679365 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Equals the XOR BINOMIAL transform of A099898. Also, equals the main diagonal of the XOR difference triangle A099897, in which the central terms of the rows form the powers of 4. See A099884 for the definitions of XOR difference triangle and the XOR BINOMIAL transform.
LINKS
FORMULA
a(n) = SumXOR_{k=0..n} (C(n-k+[k/2], [k/2])mod 2)*2^k for n>=0. a(n) = SumXOR_{i=0..n} (C(n, i)mod 2)*A099898(n-i), where SumXOR is the analog of summation under the binary XOR operation and C(i, j)mod 2 = A047999(i, j).
PROG
(PARI) {a(n)=local(B); B=0; for(k=0, n, B=bitxor(B, binomial(n-k+k\2, k\2)%2*4^k)); B}
CROSSREFS
Sequence in context: A271282 A203287 A296720 * A269566 A271492 A202462
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 30 2004
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)