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).

4, 48, 8, 204, 112, 24, 680, 384, 56, 0, 1660, 1072, 448, 76, 8, 3416, 2392, 400, 56, 0, 0, 6348, 5236, 1840, 504, 40, 0, 0, 11048, 8624, 2800, 408, 24, 0, 0, 0, 17708, 14976, 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

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, May 18 2020

Keywords

• nonn
• tabl

Comments

No formula is known.

For further illustrations see A331452.

Examples

			Triangle begins:
      4;
     48,     8;
    204,   112,    24;
    680,   384,    56,    0;
   1660,  1072,   448,   76,    8;
   3416,  2392,   400,   56,    0,   0;
   6348,  5236,  1840,  504,   40,   0,  0;
  11048,  8624,  2800,  408,   24,   0,  0, 0;
  17708, 14976,  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;
  57360, 47160, 13856, 2272,  296,  16,  0, 0, 0, 0, 0, 0;
  79108, 73572, 30800, 7788, 1152, 200, 16, 0, 0, 0, 0, 0, 0;
...
		

Links

• Scott R. Shannon, Data for triangles A334691 and A334699
• Scott R. Shannon, Colored illustration for n = 2
• Scott R. Shannon, Image showing the k-sided cells for n = 10.
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 20.

Crossrefs

Cf. A255011 (row sums), A331452, A331449, A334690, A334691, A334695, A334696, A334700.

Extensions

a(29) and beyond by Scott R. Shannon, Feb 18 2021