A108359 A symmetric number triangle based on floor((n+2)/2).

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 14, 7, 1, 1, 9, 28, 28, 9, 1, 1, 11, 47, 76, 47, 11, 1, 1, 13, 71, 163, 163, 71, 13, 1, 1, 15, 100, 301, 433, 301, 100, 15, 1, 1, 17, 134, 502, 961, 961, 502, 134, 17, 1, 1, 19, 173, 778, 1879, 2515, 1879, 778, 173, 19, 1, 1, 21, 217, 1141

Offset

0,5

Comments

Row sums are A108360. Diagonal sums are A108361.

Links

Table of n, a(n) for n=0..69.

Formula

Number triangle T(n,k) = Sum_{j=0..n-k} binomial(k,j)*binomial(n-j,k)*floor((j+2)/2). As a square array read by antidiagonals, T(n,k) = Sum_{j=0..n} binomial(k,j)*binomial(n+k-j,k)*floor((j+2)/2).

Example

Rows begin
  1;
  1,  1;
  1,  3,  1;
  1,  5,  5,  1;
  1,  7, 14,  7,  1;
  1,  9, 28, 28,  9,  1;
  1, 11, 47, 76, 47, 11,  1;
As a square array read by antidiagonals, rows start
  1,  1,   1,   1,    1,    1, ...
  1,  3,   5,   7,    9,   11, ...
  1,  5,  14,  28,   47,   71, ...
  1,  7,  28,  76,  163,  301, ...
  1,  9,  47, 163,  433,  961, ...
  1, 11,  71, 301,  961, 2515, ...
  1, 13, 100, 502, 1879, 5695, ...

Crossrefs

Sequence in context: A326792 A144461 A106597 * A100936 A086620 A338934

Adjacent sequences: A108356 A108357 A108358 * A108360 A108361 A108362

Keyword

easy,nonn,tabl

Author

Paul Barry, May 31 2005

Status

approved