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A339179 Irregular triangle read by rows: for n >= 2, 2 <= k <= floor(n/2) + 1, T(n,k) = the number of semi-meanders with n top arches, a first arch of length one and k arch groupings. 0
1, 1, 1, 1, 2, 2, 4, 4, 2, 10, 10, 4, 24, 24, 14, 4, 66, 66, 34, 8, 174, 174, 106, 42, 8, 504, 504, 284, 98, 16, 1406, 1406, 878, 390, 114, 16, 4210, 4210, 2486, 1002, 258, 32, 12198, 12198, 7738, 3652, 1270, 290, 32, 37378, 37378, 22714, 9962, 3140, 642, 64, 111278, 111278, 71370, 34986, 13370, 3794, 706, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

LINKS

Table of n, a(n) for n=2..65.

FORMULA

T(2,2) = T(3,2) = 1.

For n >= 4, T(n,2) = T(n,3) = A000682(n-2).

For n >= 6 and k >= 4, T(n,k) = Sum {x = k-1..floor(n/2)} (A259689(T(n-2,x))).

For n >= 4, A301620(n-3) = Sum {k = 4..floor((n+2)/2)} (T(n,k)).

EXAMPLE

For n = 6:   /\ = arch of length one;

       /\             /\             /\             /\

      /  \           //\\           /  \           //\\       4 with 2 groupings

     /  /\\         //  \\         /    \         ///\\\

    /  /  \\       //  /\\\       //\  /\\       ////\\\\

/\ //\//\/\\\, /\ ///\//\\\\, /\ ///\\//\\\, /\ /////\\\\\,

         /\                                              /\

        //\\              /\         /\                 /  \  4 with 3 groupings

       ///\\\       /\   //\\       //\\   /\          //\  \

/\ /\ ////\\\\, /\ //\\ ///\\\, /\ ///\\\ //\\, /\ /\ ///\\/\\,

           /\                                                 2 with 4 groupings

          /  \       /\      /\

/\ /\ /\ //\/\\, /\ //\\ /\ //\\,             T(6,2) = 4, T(6,3) = 4, T(6,4) = 2;

Irregular triangle begins:

    n\k (2) (3) (4) (5) (6)

    2:   1

    3:   1

    4:   1   1

    5:   2   2

    6:   4   4   2

    7:   10  10  4

    8:   24  24  14  4

    9:   66  66  34  8

   10:   174 174 106 42  8

         ...

CROSSREFS

Cf. A259689, A301620, Row sums: A000682(n-1).

Sequence in context: A290633 A038674 A330639 * A182923 A263856 A090277

Adjacent sequences:  A339176 A339177 A339178 * A339180 A339181 A339182

KEYWORD

nonn,tabf

AUTHOR

Roger Ford, Nov 26 2020

STATUS

approved

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Last modified June 12 16:18 EDT 2021. Contains 344959 sequences. (Running on oeis4.)