A053201 Pascal's triangle (excluding first, last element of each row) read by rows, row n read mod n.

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, 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, 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

Offset: 2

Author

Asher Auel, Dec 12 1999

Keywords

• nonn
• nice
• tabl
• look

Comments

Prime numbered rows contain all zeros.

Examples

			0; 0,0; 0,2,0; 0,0,0,0; 0,3,2,3,0; ...
row 6 = 6 mod 6, 15 mod 6, 20 mod 6, 15 mod 6, 6 mod 6 = 0, 3, 2, 3, 0
		

Links

• T. D. Noe, Rows n=2..100 of triangle, flattened

Crossrefs

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

Cf. A053214 (central terms).

Programs

Haskell

a053201 n k = a053201_tabl !! (n-2) !! (k-1)
a053201_row n = a053201_tabl !! (n-2)
a053201_tabl = zipWith (map . (flip mod)) [2..] a014410_tabl
-- Reinhard Zumkeller, Aug 17 2013

Mathematica

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 *)

Formula

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

Extensions

a(62) and a(68) corrected by T. D. Noe, Feb 08 2008