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

2,5

Comments

Prime numbered rows contain all zeros.

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Cf. A053214 (central terms).

Sequence in context: A280843 A221146 A083935 * A028605 A319532 A317576

Adjacent sequences: A053198 A053199 A053200 * A053202 A053203 A053204

Keyword

nonn,nice,tabl,look

Author

Asher Auel, Dec 12 1999

Extensions

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

Status

approved