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A334691 Irregular triangle read by rows: T(n,k) (n >= 1, 2 <= k <= 2*n) = number of interior vertices in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter) where k lines meet.

%I A334691 #28 Nov 07 2023 20:41:48
%S A334691 1,20,8,1,204,32,8,0,1,616,152,20,8,4,0,1,2428,252,36,16,4,0,0,0,1,
%T A334691 3968,572,156,72,16,8,4,0,4,0,1,11164,900,120,52,16,8,4,0,0,0,0,0,1,
%U A334691 16884,1712,396,132,40,20,8,8,8,0,0,0,0,0,1,30116,2536,600,140,60,24,8,20,8,0,0,0,0,0,0,0,1
%N A334691 Irregular triangle read by rows: T(n,k) (n >= 1, 2 <= k <= 2*n) = number of interior vertices in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter) where k lines meet.
%C A334691 No formula is known.
%H A334691 Scott R. Shannon, <a href="/A334691/a334691.txt">Data for triangles A334691 and A334699</a>
%H A334691 Scott R. Shannon, <a href="/A331452/a331452_12.png">Colored illustration for n = 2</a>
%H A334691 Scott R. Shannon, <a href="/A334697/a334697.png">Illustration for n=3 showing interior vertices color-coded according to multiplicity.</a>
%e A334691 Triangle begins:
%e A334691 1;
%e A334691 20,8,1;
%e A334691 204,32,8,0,1;
%e A334691 616,152,20,8,4,0,1;
%e A334691 2428,252,36,16,4,0,0,0,1;
%e A334691 3968,572,156,72,16,8,4,0,4,0,1;
%e A334691 11164,900,120,52,16,8,4,0,0,0,0,0,1;
%e A334691 16884,1712,396,132,40,20,8,8,8,0,0,0,0,0,1;
%e A334691 30116,2536,600,140,60,24,8,20,8,0,0,0,0,0,0,0,1;
%e A334691 43988,4056,948,312,84,56,52,20,,8,0,0,4,0,0,0,0,0,1;
%e A334691 82016,4660,580,228,48,84,4,4,4,8,4,0,0,0,0,0,0,0,0,0,1;
%e A334691 90088,8504,1840,780,424,128,68,32,32,0,0,8,24,0,0,0,4,0,0,0,0,0,1;
%e A334691 168360,8284,1056,396,128,100,52,12,4,4,4,8,4,0,0,0,0,0,0,0,0,0,0,0,1;
%e A334691 202332,13144,2980,924,256,144,140,60,44,4,0,8,8,8,0,0,4,0,0,0,0,0,0,0,0,0,1;
%e A334691 ...
%Y A334691 Cf. A255011, A331449, A334690 (row sums), A334692 (column k=2), A334693 (k=3), A334694-A334699.
%K A334691 nonn,tabf
%O A334691 1,2
%A A334691 _Scott R. Shannon_ and _N. J. A. Sloane_, May 18 2020