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Periodic Pascal array, read by upward antidiagonals.
1

%I #22 Dec 08 2023 09:57:47

%S 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,

%T 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,

%U 1,1,10,36,56,35,6,1,6,1,1,1,1

%N Periodic Pascal array, read by upward antidiagonals.

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

%H John Tyler Rascoe, <a href="/A085476/b085476.txt">Antidiagonals n = 0..139, flattened</a>

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

%e Rows begin:

%e n\k | 0 1 2 3 4 5

%e ----+------------

%e 0 | 1 1 1 1 1 1 ...

%e 1 | 1 1 1 1 1 1 ...

%e 2 | 1 2 1 1 2 1 ...

%e 3 | 1 3 3 1 1 3 ...

%e 4 | 1 4 6 4 1 1 ...

%o (Python)

%o from math import comb

%o def A085476(n,k): return(comb(n,k%(n+1))) # _John Tyler Rascoe_, Dec 01 2023

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

%K easy,nonn,tabl

%O 0,8

%A _Paul Barry_, Jul 02 2003