A053203 Pascal's triangle (excluding first, last three elements of each row) read by rows, row n read mod n.

2, 0, 0, 0, 6, 0, 3, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 7, 2, 7, 0, 7, 0, 5, 0, 3, 10, 0, 0, 10, 3, 0, 5, 0, 12, 0, 8, 0, 6, 0, 8, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 2, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 6

Author

Asher Auel, Dec 12 1999

Keywords

• nonn
• nice
• tabl

Comments

Prime numbered rows contain all zeros.

Examples

			Triangle begins:
  2;
  0,0;
  0,6,0;
  3,0,0,3;
  0,0,2,0,0;
  ...
row 9 = 84 mod 9, 126 mod 9, 126 mod 9, 84 mod 9, = 3, 0, 0, 3.
		

Links

• T. D. Noe, Rows n=6..100 of triangle, flattened

Crossrefs

Row sums give A053206.

Cf. A053200, A053201, A053203, A007318 (Pascal's triangle).

Programs

Haskell

a053203 n k = a053203_tabl !! (n - 6) !! k
a053203_row n = a053203_tabl !! (n - 6)
a053203_tabl = zipWith (\k row -> take (k - 5) $ drop 3 row)
                       [6..] $ drop 6 a053200_tabl
-- Reinhard Zumkeller, Jan 24 2014

Mathematica

Table[Mod[Binomial[n, k], n], {n, 6, 20}, {k, 3, n-3}] // Flatten (* Jean-François Alcover, Jan 17 2014 *)

Extensions

a(30) corrected by T. D. Noe, Feb 08 2008