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

Author

Alois P. Heinz, Nov 21 2017

Keywords

• nonn
• tabf

Examples

			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;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..18, flattened
• Wikipedia, Arithmetic progression
• Index entries related to non-averaging sequences

Crossrefs

Column k=0 gives A295370.

Row sums give A000142.

Cf. A162982, A289207.