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

0,8

Comments

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

Links

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

Formula

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

Example

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 ...

Prog

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

Crossrefs

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

Sequence in context: A178239 A260534 A350103 * A124944 A094392 A111946

Adjacent sequences: A085473 A085474 A085475 * A085477 A085478 A085479

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 02 2003

Status

approved