A379998 Irregular triangle read by rows: T(n,k) is number of sequences of length k over {0,1,...,n-1} containing no two consecutive blocks with the same average, n >= 1, 0 <= k <= A379914(n).

1, 1, 1, 2, 2, 2, 1, 3, 6, 8, 1, 4, 12, 28, 38, 50, 24, 6, 1, 5, 20, 64, 148, 316, 370, 340, 152, 38, 1, 6, 30, 126, 406, 1142, 2142, 3380, 4022, 3910, 2794, 2048, 988, 496, 234, 82, 14, 10, 4, 2, 1, 7, 42, 216, 898, 3314, 9014, 21760, 41026, 63898, 78204, 87820, 71434, 53984, 34232, 16716, 6400, 2346, 644, 148, 12

Offset: 1

Author

Pontus von Brömssen, Jan 09 2025

Keywords

• nonn
• tabf

Comments

See A379914 for details.

A sequence, its reversal, and its complement (where all terms x are replaced by n-1-x) are all counted.

Examples

			Triangle begins:
  1, 1;
  1, 2,  2,  2;
  1, 3,  6,  8;
  1, 4, 12, 28,  38,  50,  24,   6;
  1, 5, 20, 64, 148, 316, 370, 340, 152, 38;
  ...
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..139 (rows 1..9)

Crossrefs

Cf. A245996, A379914, A379999, A380000.

Formula

T(n,0) = 1.

T(n,1) = n.

T(n,2) = n*(n-1) for n >= 2.

T(n,3) = A245996(n-1) for n >= 2.

Empirically: T(n,4) = T(n-1,4) + T(n-2,4) - T(n-5,4) - T(n-6,4) - T(n-7,4) + T(n-8,4) + T(n-9,4) + T(n-10,4) - T(n-13,4) - T(n-14,4) + T(n-15,4) for n >= 19.