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

1,1

Comments

No formula is known.

For further illustrations see A331452.

Links

Table of n, a(n) for n=1..66.

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.

Example

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;
...

Crossrefs

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

Sequence in context: A182102 A052105 A010293 * A358885 A358889 A225987

Adjacent sequences: A334696 A334697 A334698 * A334700 A334701 A334702

Keyword

nonn,tabl

Author

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

Extensions

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

Status

approved