A053201 - OEIS

%I #17 Oct 27 2023 22:00:45

%S 0,0,0,0,2,0,0,0,0,0,0,3,2,3,0,0,0,0,0,0,0,0,4,0,6,0,4,0,0,0,3,0,0,3,

%T 0,0,0,5,0,0,2,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,6,4,3,0,0,0,3,4,6,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,7,0,7,0,7,2,7,0,7,0,7,0,0,0,5,0,3,10,0,0,10,3,0,5,0

%N Pascal's triangle (excluding first, last element of each row) read by rows, row n read mod n.

%C Prime numbered rows contain all zeros.

%H T. D. Noe, <a href="/A053201/b053201.txt">Rows n=2..100 of triangle, flattened</a>

%F T(n,k) = A014410(n,k) mod n, k=1..n-1.

%e 0; 0,0; 0,2,0; 0,0,0,0; 0,3,2,3,0; ...

%e row 6 = 6 mod 6, 15 mod 6, 20 mod 6, 15 mod 6, 6 mod 6 = 0, 3, 2, 3, 0

%t row[n_] := Table[ Mod[ Binomial[n, k], n], {k, 1, n-1}]; Table[row[n], {n, 2, 15}] // Flatten (* _Jean-François Alcover_, Aug 12 2013 *)

%o (Haskell)

%o a053201 n k = a053201_tabl !! (n-2) !! (k-1)

%o a053201_row n = a053201_tabl !! (n-2)

%o a053201_tabl = zipWith (map . (flip mod)) [2..] a014410_tabl

%o -- _Reinhard Zumkeller_, Aug 17 2013

%Y Row sums give A053205. Cf. A053200, A053202, A053203, A007318 (Pascal's triangle)

%Y Cf. A053214 (central terms).

%K nonn,nice,tabl,look

%O 2,5

%A _Asher Auel_, Dec 12 1999

%E a(62) and a(68) corrected by _T. D. Noe_, Feb 08 2008