A143086 Triangle read by rows: T(n,k) = 2^(k + 1) - 1 if k < = floor(n/2), otherwise 2^(n - k + 1) - 1, for 0 <= k <= n.

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 7, 3, 1, 1, 3, 7, 7, 3, 1, 1, 3, 7, 15, 7, 3, 1, 1, 3, 7, 15, 15, 7, 3, 1, 1, 3, 7, 15, 31, 15, 7, 3, 1, 1, 3, 7, 15, 31, 31, 15, 7, 3, 1, 1, 3, 7, 15, 31, 63, 31, 15, 7, 3, 1, 1, 3, 7, 15, 31, 63, 63, 31, 15, 7, 3, 1, 1, 3, 7, 15, 31, 63, 127, 63, 31, 15, 7, 3, 1

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Oct 16 2008

Keywords

• nonn
• tabl
• easy
• less

Examples

			Triangle begins:
  {1},
  {1,  1},
  {1,  3,  1},
  {1,  3,  3,  1},
  {1,  3,  7,  3,  1},
  {1,  3,  7,  7,  3,  1},
  {1,  3,  7, 15,  7,  3,  1},
  {1,  3,  7, 15, 15,  7,  3,  1},
  {1,  3,  7, 15, 31, 15,  7,  3,  1},
  {1,  3,  7, 15, 31, 31, 15,  7,  3,  1},
  {1,  3,  7, 15, 31, 63, 31, 15,  7,  3,  1}
		

Crossrefs

Cf. A077866 (row sums).

Programs

Mathematica

Table[Table[If[m <= Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1], {m, 0, n}], {n, 0, 10}] // Flatten

Extensions

Offset changed to 0 by Georg Fischer, Jun 08 2023