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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} (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)*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+[k/2], [k/2]) * 2^k.

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}; - Paul Barry, May 10 2005

a(n)=Sum_{k, 0<=k<=2n}A106344(2n,k)*2^(2n-k). [From 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 * A092284 A024459 A001645

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 April 23 18:45 EDT 2017. Contains 285329 sequences.