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 A099902 Multiplies by 2 and shifts right under the XOR BINOMIAL transform (A099901). 5
 1, 3, 7, 11, 23, 59, 103, 139, 279, 827, 1895, 2955, 5655, 14395, 24679, 32907, 65815, 197435, 460647, 723851, 1512983, 3881019, 6774887, 9142411, 18219287, 54002491, 123733863, 192940939, 369104407, 939538491, 1610637415, 2147516555 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. Bisection of A101624. - Paul Barry, May 10 2005 LINKS Robert Israel, Table of n, a(n) for n = 0..3290 FORMULA a(n) = SumXOR_{k=0..n} (binomial(n-k+floor(k/2), floor(k/2)) mod 2)*2^k for n >= 0. 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). a(n) = Sum_{k=0..n} A047999(n-k+floor(k/2), floor(k/2)) * 2^k. From Paul Barry, May 10 2005: (Start) a(n) = Sum_{k=0..2n} (binomial(k, 2n-k) mod 2)*2^(2n-k); a(n) = Sum_{k=0..n} (binomial(2n-k, k) mod 2)*2^k. (End) a(n) = Sum_{k=0..2n} A106344(2n,k)*2^(2n-k). - Philippe Deléham, Dec 18 2008 MAPLE a:= n -> add((binomial(n-k+floor(k/2), floor(k/2)) mod 2)*2^k, k=0..n): map(a, [\$0..100]); # Robert Israel, Jan 24 2016 PROG (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} (PARI) a(n)=sum(k=0, n, binomial(n-k+k\2, k\2)%2*2^k) CROSSREFS Cf. A099884, A099900, A099901. Sequence in context: A116606 A188132 A139814 * A336897 A316962 A092284 Adjacent sequences:  A099899 A099900 A099901 * A099903 A099904 A099905 KEYWORD eigen,nonn AUTHOR Paul D. Hanna, Oct 30 2004 STATUS approved

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Last modified May 5 19:09 EDT 2021. Contains 343573 sequences. (Running on oeis4.)