login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 * A316962 A092284 A024459

Adjacent sequences:  A099899 A099900 A099901 * A099903 A099904 A099905

KEYWORD

eigen,nonn

AUTHOR

Paul D. Hanna, Oct 30 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 3 09:17 EDT 2020. Contains 335417 sequences. (Running on oeis4.)