A295390 Number T(n,k) of permutations of [n] having exactly k consecutive 3-term arithmetic progressions; triangle T(n,k), n>=0, 0<=k<=max(n-2,0), read by rows.

1, 1, 2, 4, 2, 18, 4, 2, 80, 34, 4, 2, 482, 196, 36, 4, 2, 3280, 1418, 292, 44, 4, 2, 26244, 11292, 2426, 304, 48, 4, 2, 231148, 106132, 22156, 3010, 372, 56, 4, 2, 2320130, 1046176, 225804, 32308, 3892, 424, 60, 4, 2, 25238348, 11679626, 2585080, 366484, 42176, 4540, 472, 68, 4, 2

Offset

0,3

Links

Alois P. Heinz, Rows n = 0..18, flattened

Wikipedia, Arithmetic progression

Index entries related to non-averaging sequences

Example

Triangle T(n,k) begins:
        1;
        1;
        2;
        4,       2;
       18,       4,      2;
       80,      34,      4,     2;
      482,     196,     36,     4,    2;
     3280,    1418,    292,    44,    4,   2;
    26244,   11292,   2426,   304,   48,   4,  2;
   231148,  106132,  22156,  3010,  372,  56,  4, 2;
  2320130, 1046176, 225804, 32308, 3892, 424, 60, 4, 2;
  ...

Crossrefs

Column k=0 gives A295370.

Row sums give A000142.

Cf. A162982, A289207.

Sequence in context: A326723 A227924 A100944 * A059890 A295640 A210457

Adjacent sequences: A295387 A295388 A295389 * A295391 A295392 A295393

Keyword

nonn,tabf

Author

Alois P. Heinz, Nov 21 2017

Status

approved