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A208355 Right edge of the triangle in A208101. 6

%I

%S 1,1,1,2,2,5,5,14,14,42,42,132,132,429,429,1430,1430,4862,4862,16796,

%T 16796,58786,58786,208012,208012,742900,742900,2674440,2674440,

%U 9694845,9694845,35357670,35357670,129644790,129644790,477638700,477638700,1767263190

%N Right edge of the triangle in A208101.

%H Reinhard Zumkeller, <a href="/A208355/b208355.txt">Table of n, a(n) for n = 0..1000</a>

%H D. Levin, L. Pudwell, M. Riehl, A. Sandberg, <a href="http://www.etsu.edu/cas/math/pp2014/documents/talks/riehl.pdf">Pattern Avoidance on k-ary Heaps</a>, Slides of Talk, 2014.

%F a(n) = A000108(floor((n+1)/2)), where A000108 = Catalan numbers.

%F a(n) = A208101(n,n).

%F a(n) = abs(A099363(n)).

%F Conjecture: -(n+3)*(n-2)*a(n) -4*a(n-1) +4*(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Aug 04 2015

%p A208355_list := proc(len) local D, b, h, R, i, k;

%p D := [seq(0, j=0..len+2)]; D[1] := 1; b := true; h := 2; R := NULL;

%p for i from 1 to 2*len do

%p if b then

%p for k from h by -1 to 2 do D[k] := D[k] - D[k-1] od;

%p h := h + 1; R := R, abs(D[2]);

%p else

%p for k from 1 by 1 to h do D[k] := D[k] + D[k+1] od;

%p fi;

%p b := not b:

%p od;

%p return R

%p end:

%p A208355_list(38); # _Peter Luschny_, Dec 19 2017

%t T[_, 0] = 1; T[n_, 1] := n; T[n_, n_] := T[n - 1, n - 2]; T[n_, k_] /; 1 < k < n := T[n, k] = T[n - 1, k] + T[n - 1, k - 2];

%t a[n_] := T[n, n];

%t Table[a[n], {n, 0, 40}] (* _Jean-Fran├žois Alcover_, Feb 03 2018, from A208101 *)

%o (Haskell)

%o a208355 n = a208101 n n

%o a208355_list = map last a208101_tabl

%o (MAGMA) [Ceiling(Catalan(n div 2)): n in [1..40]]; // _Vincenzo Librandi_, Feb 18 2014

%K nonn

%O 0,4

%A _Reinhard Zumkeller_, Mar 04 2012

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Last modified February 19 03:29 EST 2018. Contains 299330 sequences. (Running on oeis4.)