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A334699 Triangle read by rows: T(n,k) (n >= 1, 3 <= k <= n+2) = number of k-sided cells in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).

%I A334699 #31 Jan 14 2023 10:56:18
%S A334699 4,48,8,204,112,24,680,384,56,0,1660,1072,448,76,8,3416,2392,400,56,0,
%T A334699 0,6348,5236,1840,504,40,0,0,11048,8624,2800,408,24,0,0,0,17708,14976,
%U A334699 4960,1004,96,4,0,0,0,27520,22200,7104,1288,136,8,0,0,0,0,40388,35832,15080,3808,488,60,0,0,0,0,0
%N A334699 Triangle read by rows: T(n,k) (n >= 1, 3 <= k <= n+2) = number of k-sided cells in the n-th figure shown in A255011 (meaning the figure with 4n points on the perimeter).
%C A334699 No formula is known.
%C A334699 For further illustrations see A331452.
%H A334699 Scott R. Shannon, <a href="/A334691/a334691.txt">Data for triangles A334691 and A334699</a>
%H A334699 Scott R. Shannon, <a href="/A331452/a331452_12.png">Colored illustration for n = 2</a>
%H A334699 Scott R. Shannon, <a href="/A334699/a334699.png">Image showing the k-sided cells for n = 10</a>.
%H A334699 N. J. A. Sloane, <a href="https://arxiv.org/abs/2301.03149">"A Handbook of Integer Sequences" Fifty Years Later</a>, arXiv:2301.03149 [math.NT], 2023, p. 20.
%e A334699 Triangle begins:
%e A334699       4;
%e A334699      48,     8;
%e A334699     204,   112,    24;
%e A334699     680,   384,    56,    0;
%e A334699    1660,  1072,   448,   76,    8;
%e A334699    3416,  2392,   400,   56,    0,   0;
%e A334699    6348,  5236,  1840,  504,   40,   0,  0;
%e A334699   11048,  8624,  2800,  408,   24,   0,  0, 0;
%e A334699   17708, 14976,  4960, 1004,   96,   4,  0, 0, 0;
%e A334699   27520, 22200,  7104, 1288,  136,   8,  0, 0, 0, 0;
%e A334699   40388, 35832, 15080, 3808,  488,  60,  0, 0, 0, 0, 0;
%e A334699   57360, 47160, 13856, 2272,  296,  16,  0, 0, 0, 0, 0, 0;
%e A334699   79108, 73572, 30800, 7788, 1152, 200, 16, 0, 0, 0, 0, 0, 0;
%e A334699 ...
%Y A334699 Cf. A255011 (row sums), A331452, A331449, A334690, A334691, A334695, A334696, A334700.
%K A334699 nonn,tabl
%O A334699 1,1
%A A334699 _Scott R. Shannon_ and _N. J. A. Sloane_, May 18 2020
%E A334699 a(29) and beyond by _Scott R. Shannon_, Feb 18 2021