A347433 - cp's OEIS frontend

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.

%I A347433 #18 Oct 09 2021 16:06:01
%S A347433 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,
%T A347433 17,30,43,56,4,18,32,46,60,74,4,19,34,49,64,79,4,20,36,52,68,84,100,4,
%U A347433 21,38,55,72,89,106,4,22,40,58,76,94,112,130,4,23,42,61,80,99
%N 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.
%F A347433 For  n >= 2 and k = 2..floor((n+2)/2), T(n,k) = 4 + (n+2)*(k-2).
%e A347433 n = number of top arches, k = number of exterior top arches:
%e A347433 n\k  2   3   4   5   6
%e A347433 2:   4
%e A347433 3:   4
%e A347433 4:   4   10
%e A347433 5:   4   11
%e A347433 6:   4   12  20
%e A347433 7:   4   13  22
%e A347433 8:   4   14  24  34
%e A347433 9:   4   15  26  37
%e A347433 10:  4   16  28  40  52
%e A347433 Length of each arch = 1 + number of arches covered:
%e A347433 Top arches of a given semi-meander:       Arch splitting generated
%e A347433 n = 5, k = 2                              semi-meanders (6 top arches):
%e A347433      1     1    = 2 exterior arches                /\
%e A347433            /\                                     //\\
%e A347433      /\   //\\                                   ///\\\
%e A347433     //\\ ///\\\                           /\ /\ ////\\\\
%e A347433     21   321    = 9 length of top arches  1  1  4321     = 12 length of top arches
%e A347433                                             /\
%e A347433                                            //\\   /\
%e A347433                                           ///\\\ //\\ /\
%e A347433                                           321    21   1  = 10 length of top arches
%e A347433     T(5,2) = 4 + (5+2)(2-2) = 4 --------------------------- 4 = (12+10) - (2 * 9);
%e A347433 Top arches of given semi meander:
%e A347433 n = 5, k = 3                                    /\
%e A347433     1   1    1   = 3 exterior arches           /  \
%e A347433         /\   /\                               /    \
%e A347433     /\ //\\ //\\                             //\  /\\
%e A347433     1  21   21   = 7 length top arches   /\ ///\\//\\\
%e A347433                                          1  521  21     = 12 length of top arches
%e A347433                                                    /\
%e A347433                                           /\      //\\
%e A347433                                          //\\ /\ ///\\\
%e A347433                                          21   1  321    = 10 length of top arches
%e A347433                                             /\
%e A347433                                            /  \
%e A347433                                           /  /\\
%e A347433                                          //\//\\\ /\ /\
%e A347433                                          41 21    1  1  = 10 length of top arches
%e A347433     T(5,3) = 4 + (5+2)(3-2) = 11 --------------------- 11 = (12+10+10) - (3 * 7).
%Y A347433 Cf. A345747.
%K A347433 nonn,tabf
%O A347433 2,1
%A A347433 _Roger Ford_, Sep 01 2021
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