OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..1000
B. R. Hodgson, Letter to N. J. A. Sloane, Oct. 1991
B. R. Hodgson, On some number sequences related to the parity of binomial coefficients, Fib. Quart., 30 (1992), 35-47.
FORMULA
a(n) = Sum_{r=0..n/2} (binomial(n-r,r)_{mod 2} * 2^(floor(n/2)-r). - N. J. A. Sloane, Jul 14 2015
MAPLE
b2:=(n, k)->binomial(n, k) mod 2;
H:=n->add(b2(n-r, r)*2^( floor(n/2)-r ), r=0..floor(n/2));
[seq(H(n), n=0..30)]; # N. J. A. Sloane, Jul 14 2015
PROG
(Haskell)
a006921 = sum . zipWith (*)
a000079_list . map (flip mod 2) . reverse . a011973_row
-- Reinhard Zumkeller, Jul 14 2015
(Python)
def A006921(n): return sum(int(not r & ~(n-r))*2**(n//2-r) for r in range(n//2+1)) # Chai Wah Wu, Jun 20 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved