A391113 Triangle read by rows: T(n,k) is the area of the irregular hexagon, rounded to the nearest integer, where its vertices lie on the co-vertices and the endpoints of the two latus rectums of an ellipse, where n and k are respectively the integer major and minor axes with n >= 2 and k >= 1.

5, 8, 15, 10, 21, 28, 12, 26, 38, 43, 14, 30, 47, 60, 61, 16, 34, 54, 72, 84, 80, 18, 39, 61, 83, 101, 111, 102, 20, 43, 68, 93, 116, 134, 141, 125, 22, 47, 74, 103, 130, 154, 170, 173, 149, 24, 51, 81, 112, 143, 171, 194, 209, 207, 175, 26, 55, 87, 121, 155

Offset

2,1

Comments

From n = 3, all terms T(n,1) are in arithmetic progression of initial term 8 and common difference 2.

Links

Table of n, a(n) for n=2..61.

Formula

T(n,k) = round(2*sqrt(n^2-k^2)*(k+k^2/n)).

Example

Triangle begins:
  n/k    1   2   3    4    5    6    7    8    9   10   11
  --------------------------------------------------------
   2 |   5
   3 |   8  15
   4 |  10  21  28
   5 |  12  26  38   43
   6 |  14  30  47   60   61
   7 |  16  34  54   72   84   80
   8 |  18  39  61   83  101  111  102
   9 |  20  43  68   93  116  134  141  125
  10 |  22  47  74  103  130  154  170  173  149
  11 |  24  51  81  112  143  171  194  209  207  175
  12 |  26  55  87  121  155  187  216  239  250  243  202

Prog

(PARI) row(n)=vector(n-1, k, round(2*sqrt(n^2-k^2)*(k+k^2/n)));

Crossrefs

Cf. A108126, A386539.

Sequence in context: A246319 A302649 A286835 * A112269 A314527 A314528

Adjacent sequences: A391110 A391111 A391112 * A391114 A391115 A391116

Keyword

nonn,tabl

Author

Claude H. R. Dequatre, Jan 25 2026

Status

approved