login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192481 a(n) = Sum_{i=1..n-1} (2^i*C(i)-a(i)) * (2^(n-i)*C(n-i)-a(n-i)), a(0)=0, a(1)=1, where C(i)=A000108(i-1) are Catalan numbers. 2

%I

%S 1,1,6,29,162,978,6156,40061,267338,1819238,12576692,88079378,

%T 623581332,4455663876,32090099352,232711721757,1697799727066,

%U 12452943237342,91774314536100,679234371006982,5046438870909244,37623611703611452,281391143518722728

%N a(n) = Sum_{i=1..n-1} (2^i*C(i)-a(i)) * (2^(n-i)*C(n-i)-a(n-i)), a(0)=0, a(1)=1, where C(i)=A000108(i-1) are Catalan numbers.

%C a(n) is the number of rows with the value false in the truth tables of all bracketed m-implication, case (i), with n distinct variables.

%H G. C. Greubel, <a href="/A192481/b192481.txt">Table of n, a(n) for n = 1..1000</a>

%H Volkan Yildiz, <a href="http://arxiv.org/abs/1203.4645">Counting false entries in truth tables of bracketed formulas connected by m-implication</a>, arXiv:1203.4645 [math.CO], 2012.

%H Volkan Yildiz, <a href="http://arxiv.org/abs/1205.5595">General combinatorical structure of truth tables of bracketed formulas connected by implication</a>, arXiv:1205.5595 [math.CO], 2012.

%F G.f.: (2 - sqrt(1-8*x) - sqrt(3 - 4*x - 2*sqrt(1-8*x)))/2.

%F For large n, a(n) is asymptotically (1-2/sqrt 10) * 2^(3n-2)/ sqrt(pi*n^3).

%p C := proc(n) binomial(2*n,n)/(n+1) ; end proc:

%p A192481 := proc(n) option remember; if n<=1 then n; else add( (2^i*C(i-1)-procname(i))*(2^(n-i)*C(n-i-1)-procname(n-i)), i=1..n-1) ; end if; end proc:

%t CoefficientList[Series[(2 - Sqrt[1 - 8*x] - Sqrt[3 - 4*x - 2*Sqrt[1 - 8*x]])/2, {x,0,50}], x] (* _G. C. Greubel_, Feb 12 2017 *)

%o (PARI) x='x+O('x^50); Vec((2-sqrt(1-8*x)-sqrt(3-4*x-2*sqrt(1-8*x)))/2) \\ _G. C. Greubel_, Feb 12 2017

%Y Cf. A000108, A186997, A192479.

%K nonn

%O 1,3

%A _Volkan Yildiz_, Jul 01 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 7 19:07 EST 2021. Contains 341928 sequences. (Running on oeis4.)