A120739 a(n) = Sum_{k=0..n} floor(C(n,k)/2).

0, 0, 1, 2, 7, 14, 30, 60, 127, 254, 510, 1020, 2046, 4092, 8188, 16376, 32767, 65534, 131070, 262140, 524286, 1048572, 2097148, 4194296, 8388606, 16777212, 33554428, 67108856, 134217724, 268435448, 536870904, 1073741808, 2147483647

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

Cf. A001316, A011848, A166454.

Sequence in context: A289377 A289408 A290519 * A221318 A221319 A221320

Adjacent sequences: A120736 A120737 A120738 * A120740 A120741 A120742

Keyword

easy,nonn

Author

Paul Barry, Jun 29 2006

Status

approved