%I
%S 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 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 21,38,55,72,89,106,4,22,40,58,76,94,112,130,4,23,42,61,80,99
%N Irregular triangle read by rows: T(n,k) is the difference between the total arch lengths of a semimeander multiplied by its number of exterior arches and total arch lengths of the semimeanders with n + 1 top arches generated by the exterior arch splitting algorithm on the given semimeander.
%F For n >= 2 and k = 2..floor((n+2)/2), T(n,k) = 4 + (n+2)*(k2).
%e n = number of top arches, k = number of exterior top arches:
%e n\k 2 3 4 5 6
%e 2: 4
%e 3: 4
%e 4: 4 10
%e 5: 4 11
%e 6: 4 12 20
%e 7: 4 13 22
%e 8: 4 14 24 34
%e 9: 4 15 26 37
%e 10: 4 16 28 40 52
%e Length of each arch = 1 + number of arches covered:
%e Top arches of a given semimeander: Arch splitting generated
%e n = 5, k = 2 semimeanders (6 top arches):
%e 1 1 = 2 exterior arches /\
%e /\ //\\
%e /\ //\\ ///\\\
%e //\\ ///\\\ /\ /\ ////\\\\
%e 21 321 = 9 length of top arches 1 1 4321 = 12 length of top arches
%e /\
%e //\\ /\
%e ///\\\ //\\ /\
%e 321 21 1 = 10 length of top arches
%e T(5,2) = 4 + (5+2)(22) = 4  4 = (12+10)  (2 * 9);
%e Top arches of given semi meander:
%e n = 5, k = 3 /\
%e 1 1 1 = 3 exterior arches / \
%e /\ /\ / \
%e /\ //\\ //\\ //\ /\\
%e 1 21 21 = 7 length top arches /\ ///\\//\\\
%e 1 521 21 = 12 length of top arches
%e /\
%e /\ //\\
%e //\\ /\ ///\\\
%e 21 1 321 = 10 length of top arches
%e /\
%e / \
%e / /\\
%e //\//\\\ /\ /\
%e 41 21 1 1 = 10 length of top arches
%e T(5,3) = 4 + (5+2)(32) = 11  11 = (12+10+10)  (3 * 7).
%Y Cf. A345747.
%K nonn,tabf
%O 2,1
%A _Roger Ford_, Sep 01 2021
