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

6,1

Comments

Prime numbered rows contain all zeros.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Row sums give A053206.

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

Sequence in context: A339016 A262679 A326390 * A158360 A309746 A094315

Adjacent sequences: A053200 A053201 A053202 * A053204 A053205 A053206

Keyword

nonn,nice,tabl

Author

Asher Auel, Dec 12 1999

Extensions

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

Status

approved