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A347433 Irregular triangle read by rows: T(n,k) is the difference between the total arch lengths of a semi-meander multiplied by its number of exterior arches and total arch lengths of the semi-meanders with n + 1 top arches generated by the exterior arch splitting algorithm on the given semi-meander. 0
4, 4, 4, 10, 4, 11, 4, 12, 20, 4, 13, 22, 4, 14, 24, 34, 4, 15, 26, 37, 4, 16, 28, 40, 52, 4, 17, 30, 43, 56, 4, 18, 32, 46, 60, 74, 4, 19, 34, 49, 64, 79, 4, 20, 36, 52, 68, 84, 100, 4, 21, 38, 55, 72, 89, 106, 4, 22, 40, 58, 76, 94, 112, 130, 4, 23, 42, 61, 80, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..71.

FORMULA

For  n >= 2 and k = 2..floor((n+2)/2), T(n,k) = 4 + (n+2)*(k-2).

EXAMPLE

n = number of top arches, k = number of exterior top arches:

n\k  2   3   4   5   6

2:   4

3:   4

4:   4   10

5:   4   11

6:   4   12  20

7:   4   13  22

8:   4   14  24  34

9:   4   15  26  37

10:  4   16  28  40  52

Length of each arch = 1 + number of arches covered:

Top arches of a given semi-meander:       Arch splitting generated

n = 5, k = 2                              semi-meanders (6 top arches):

     1     1    = 2 exterior arches                /\

           /\                                     //\\

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

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

    21   321    = 9 length of top arches  1  1  4321     = 12 length of top arches

                                            /\

                                           //\\   /\

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

                                          321    21   1  = 10 length of top arches

    T(5,2) = 4 + (5+2)(2-2) = 4 --------------------------- 4 = (12+10) - (2 * 9);

Top arches of given semi meander:

n = 5, k = 3                                    /\

    1   1    1   = 3 exterior arches           /  \

        /\   /\                               /    \

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

    1  21   21   = 7 length top arches   /\ ///\\//\\\

                                         1  521  21     = 12 length of top arches

                                                   /\

                                          /\      //\\

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

                                         21   1  321    = 10 length of top arches

                                            /\

                                           /  \

                                          /  /\\

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

                                         41 21    1  1  = 10 length of top arches

    T(5,3) = 4 + (5+2)(3-2) = 11 --------------------- 11 = (12+10+10) - (3 * 7).

CROSSREFS

Cf. A345747.

Sequence in context: A013601 A219802 A219460 * A220010 A190717 A220204

Adjacent sequences:  A347430 A347431 A347432 * A347434 A347435 A347436

KEYWORD

nonn,tabf

AUTHOR

Roger Ford, Sep 01 2021

STATUS

approved

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)