A129994 Triangle read by rows: 2*A007318 - I.

1, 2, 1, 2, 4, 1, 2, 6, 6, 1, 2, 8, 12, 8, 1, 2, 10, 20, 20, 10, 1, 2, 12, 30, 40, 30, 12, 1, 2, 14, 42, 70, 70, 42, 14, 1, 2, 16, 56, 112, 140, 112, 56, 16, 1, 2, 18, 72, 168, 252, 252, 168, 72, 18, 1

Offset

0,2

Comments

Row sums = (1, 3, 7, 15, 31, ...).

Links

Table of n, a(n) for n=0..54.

Formula

Let Pascal's triangle A007318 = P, then this is 2*P - I, I = Identity matrix.

Example

First few rows of the triangle are:
  1;
  2,  1;
  2,  4,  1;
  2,  6,  6,  1;
  2,  8, 12,  8,  1;
  2, 10, 20, 20, 10,  1;
  2, 12, 30, 40, 30, 12,  1;
  ...

Mathematica

Table[2 Binomial[n, k] - Boole[k == n], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Nov 02 2017 *)

Crossrefs

Cf. A007318.

Sequence in context: A203647 A376826 A114791 * A208755 A226441 A080246

Adjacent sequences: A129991 A129992 A129993 * A129995 A129996 A129997

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 15 2007

Extensions

Name corrected by Peter Bala, Nov 02 2017

Status

approved