OFFSET
0,4
COMMENTS
Nonzero terms = row sums of triangle A166454. - Gary W. Adamson, Oct 14 2009
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..3322
Pantelimon Stanica, Tsutomu Sasao, Jon T. Butler, Distance Duality on Some Classes of Boolean Functions, Journal of Combinatorial Mathematics and Combinatorial Computing (to appear), 2017. [Theorem 9.]
FORMULA
a(n) = (2^n - A001316(n))/2.
MATHEMATICA
Table[Sum[Floor[Binomial[n, k]/2], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, Apr 18 2019 *)
PROG
(PARI) a(n)=(2^n-2^norml2(binary(n)))/2
(PARI) {a(n) = sum(k=0, n, binomial(n, k)\2)}; \\ G. C. Greubel, Apr 18 2019
(Haskell)
a120739 n = if n < 2 then 0 else sum $ a166454_row n
-- Reinhard Zumkeller, Mar 04 2015
(Magma) [(&+[Floor(Binomial(n, k)/2): k in [0..n]]): n in [0..40]]; // G. C. Greubel, Apr 18 2019
(Sage) [sum(floor(binomial(n, k)/2) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Apr 18 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 29 2006
STATUS
approved