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A208355 Right edge of the triangle in A208101. 6
1, 1, 1, 2, 2, 5, 5, 14, 14, 42, 42, 132, 132, 429, 429, 1430, 1430, 4862, 4862, 16796, 16796, 58786, 58786, 208012, 208012, 742900, 742900, 2674440, 2674440, 9694845, 9694845, 35357670, 35357670, 129644790, 129644790, 477638700, 477638700, 1767263190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

D. Levin, L. Pudwell, M. Riehl, A. Sandberg, Pattern Avoidance on k-ary Heaps, Slides of Talk, 2014.

FORMULA

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

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

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

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

MAPLE

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

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

    for i from 1 to 2*len do

        if b then

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

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

        else

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

        fi;

        b := not b:

    od;

    return R

end:

A208355_list(38); # Peter Luschny, Dec 19 2017

PROG

(Haskell)

a208355 n = a208101 n n

a208355_list = map last a208101_tabl

(MAGMA) [Ceiling(Catalan(n div 2)): n in [1..40]]; // Vincenzo Librandi, Feb 18 2014

CROSSREFS

Sequence in context: A285013 A095014 A129996 * A099363 A106181 A098887

Adjacent sequences:  A208352 A208353 A208354 * A208356 A208357 A208358

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 04 2012

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.