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

Author

Paul Barry, Jun 29 2006

Keywords

• easy
• nonn

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.]

Crossrefs

Cf. A001316, A011848, A166454.

Programs

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

Mathematica

Table[Sum[Floor[Binomial[n,k]/2], {k,0,n}], {n,0,40}] (* G. C. Greubel, Apr 18 2019 *)

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

Sage

[sum(floor(binomial(n,k)/2) for k in (0..n)) for n in (0..40)] # G. C. Greubel, Apr 18 2019

Formula

a(n) = (2^n - A001316(n))/2.