The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A099901 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A099901

Shifts left and divides by 2 under the XOR BINOMIAL transform (A099902).
(history; published version)

#11 by Jon E. Schoenfield at Sat Jul 11 01:05:19 EDT 2015

STATUS

editing

approved

#10 by Jon E. Schoenfield at Sat Jul 11 01:05:18 EDT 2015

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 analogue analog of summation under the binary XOR operation and C(k, i)mod 2 = A047999(k, i).

STATUS

approved

editing

#9 by N. J. A. Sloane at Sun May 11 22:43:12 EDT 2014

STATUS

proposed

approved

#8 by Jon E. Schoenfield at Sun May 11 22:42:25 EDT 2014

STATUS

editing

proposed

#7 by Jon E. Schoenfield at Sun May 11 22:42:23 EDT 2014

COMMENTS

Equals the XOR BINOMIAL transform of A099902. Also, equals the left-most leftmost column of the XOR difference triangle A099900, in which the central terms of the rows forms the powers of 2.

STATUS

approved

editing

#6 by Russ Cox at Fri Mar 30 18:36:43 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 30 2004

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

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 analogue of summation under the binary XOR operation, and C(k, i)mod 2 = A047999(k, i).

KEYWORD

eigen,nonn,new

#4 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

eigen,nonn,new

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Oct 30 2004

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

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 analogue of summation under the binary XOR operation, and C(k, i)mod 2 = A047999(k, i).

KEYWORD

eigen,nonn,new

#2 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

FORMULA

a(0)=1; a(n) = SumXOR_{k=0..n-1} (C(n-1-k+[k/2],[k/2])mod2mod 2)*2^(k+1) for n>0. a(n) = SumXOR_{i=0..n} (C(n,i)mod2mod 2)*A099902(n-i), where SumXOR is the analog of summation under the binary XOR operation, and C(k,i)mod2 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}

KEYWORD

eigen,nonn,new