A143087 Triangle read by rows: T(n,k) = (2*2^min(k,n-k) - 1)*binomial(n,k).

1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 12, 42, 12, 1, 1, 15, 70, 70, 15, 1, 1, 18, 105, 300, 105, 18, 1, 1, 21, 147, 525, 525, 147, 21, 1, 1, 24, 196, 840, 2170, 840, 196, 24, 1, 1, 27, 252, 1260, 3906, 3906, 1260, 252, 27, 1, 1, 30, 315, 1800, 6510, 15876, 6510, 1800, 315, 30, 1

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Example

Triangle read by rows:
  1;
  1,  1;
  1,  6,   1;
  1,  9,   9,   1;
  1, 12,  42,  12,   1;
  1, 15,  70,  70,  15,   1;
  1, 18, 105, 300, 105,  18,  1;
  1, 21, 147, 525, 525, 147, 21, 1;
  ...

Mathematica

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

Prog

(PARI) T(n, k) = (2*2^min(k, n-k) - 1)*binomial(n, k); \\ Andrew Howroyd, Nov 19 2025

Crossrefs

Sequence in context: A189089 A132047 A140284 * A144470 A174377 A176151

Adjacent sequences: A143084 A143085 A143086 * A143088 A143089 A143090

Keyword

nonn

Author

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

Extensions

Edited by Andrew Howroyd, Nov 19 2025

Status

approved