A085476 Periodic Pascal array, read by upward antidiagonals.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 4, 3, 1, 1, 1, 1, 5, 6, 1, 2, 1, 1, 1, 6, 10, 4, 1, 1, 1, 1, 1, 7, 15, 10, 1, 3, 1, 1, 1, 1, 8, 21, 20, 5, 1, 3, 2, 1, 1, 1, 9, 28, 35, 15, 1, 4, 1, 1, 1, 1, 1, 10, 36, 56, 35, 6, 1, 6, 1, 1, 1, 1

Offset: 0

Author

Paul Barry, Jul 02 2003

Keywords

• easy
• nonn
• tabl

Comments

G.f. of binomial transform of n-th row is given by 1/((1-x)^(n+1)-x^(n+1)).

Examples

			Rows begin:
n\k | 0 1 2 3 4 5
----+------------
  0 | 1 1 1 1 1 1 ...
  1 | 1 1 1 1 1 1 ...
  2 | 1 2 1 1 2 1 ...
  3 | 1 3 3 1 1 3 ...
  4 | 1 4 6 4 1 1 ...
		

Links

• John Tyler Rascoe, Antidiagonals n = 0..139, flattened

Crossrefs

Cf. A007318, A000749, A049016, A006090, A049017.

Programs

Python

from math import comb
def A085476(n,k): return(comb(n,k%(n+1))) # John Tyler Rascoe, Dec 01 2023

Formula

Square array T(n, k) = C(n, k mod (n+1)).