A096921 Triangle array of binomial coefficients.

1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 3, 3, 6, 1, 1, 3, 4, 6, 10, 1, 1, 4, 4, 10, 10, 20, 1, 1, 4, 5, 10, 15, 20, 35, 1, 1, 5, 5, 15, 15, 35, 35, 70, 1, 1, 5, 6, 15, 21, 35, 56, 70, 126, 1, 1, 6, 6, 21, 21, 56, 56, 126, 126, 252, 1, 1, 6, 7, 21, 28, 56, 84, 126, 210, 252, 462

Offset

0,6

Links

Table of n, a(n) for n=0..77.

Formula

T(n, k) = binomial(floor((n+k)/2), floor(k/2)).

Example

Triangle begins:
      k=0  1  2  3  4  5
  n=0:  1;
  n=1:  1, 1;
  n=2:  1, 1, 2;
  n=3:  1, 1, 2, 3;
  n=4:  1, 1, 3, 3, 6;
  n=5:  1, 1, 3, 4, 6, 10;
  ...

Mathematica

T[n_, k_]=Binomial[Floor[(n+k)/2], Floor[k/2]]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] (* Stefano Spezia, Aug 23 2022 *)

Prog

(PARI) T(n, k) = binomial((n+k)\2, k\2); \\ Michel Marcus, Oct 29 2022

Crossrefs

Cf. A026010 (row sums), A016116 (diagonal sums), A001405 (main diagonal).

Sequence in context: A335545 A334997 A030111 * A308203 A275416 A037161

Adjacent sequences: A096918 A096919 A096920 * A096922 A096923 A096924

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 15 2004

Status

approved