A131404 a(n) = 2*A131402(n) - 1.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 11, 13, 11, 1, 1, 13, 27, 27, 13, 1, 1, 17, 39, 65, 39, 17, 1, 1, 19, 61, 111, 111, 61, 19, 1, 1, 23, 79, 193, 221, 193, 79, 23, 1, 1, 25, 109, 283, 433, 433, 283, 109, 25, 1, 1, 29, 133, 425, 715, 925, 715, 425, 133, 29, 1

Offset: 0

Author

Gary W. Adamson, Jul 07 2007

Keywords

• nonn
• tabl
• easy

Comments

Row sums = A131405: (1, 2, 7, 16, 37, 82, 179, ...).

Examples

			First few rows of the triangle are:
  1;
  1,  1;
  1,  5,  1;
  1,  7,  7,  1;
  1, 11, 13, 11,  1;
  1, 13, 27, 27, 13,  1;
  1, 17, 39, 65, 39, 17,  1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1274

Crossrefs

Row sums are A131405.

Cf. A131402.

Programs

Magma

/* As triangle */ [[4*Binomial(n, k) + 1 - 2*Binomial(Floor(n + k) div 2, k) - 2*Binomial(n-Floor((k+1)/2), Floor(k/2)): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Aug 10 2018

PARI

T(n,k) = if(k <= n, 4*binomial(n,k) + 1 - 2*binomial((n + k)\2, k) - 2*binomial(n-(k+1)\2, k\2), 0) \\ Andrew Howroyd, Aug 09 2018

Formula

T(n,k) = 4*binomial(n, k) + 1 - 2*binomial(floor((n + k)/2), k) - 2*binomial(n-floor((k+1)/2), floor(k/2)). - Andrew Howroyd, Aug 09 2018

Extensions

Terms a(55) and beyond from Andrew Howroyd, Aug 09 2018