A053203 - OEIS

%I #15 Oct 27 2023 22:00:45

%S 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,

%T 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,

%U 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

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

%C Prime numbered rows contain all zeros.

%H T. D. Noe, <a href="/A053203/b053203.txt">Rows n=6..100 of triangle, flattened</a>

%e Triangle begins:

%e   2;

%e   0,0;

%e   0,6,0;

%e   3,0,0,3;

%e   0,0,2,0,0;

%e   ...

%e row 9 = 84 mod 9, 126 mod 9, 126 mod 9, 84 mod 9, = 3, 0, 0, 3.

%t Table[Mod[Binomial[n, k], n], {n, 6, 20}, {k, 3, n-3}] // Flatten (* _Jean-François Alcover_, Jan 17 2014 *)

%o (Haskell)

%o a053203 n k = a053203_tabl !! (n - 6) !! k

%o a053203_row n = a053203_tabl !! (n - 6)

%o a053203_tabl = zipWith (\k row -> take (k - 5) $ drop 3 row)

%o                        [6..] $ drop 6 a053200_tabl

%o -- _Reinhard Zumkeller_, Jan 24 2014

%Y Row sums give A053206.

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

%K nonn,nice,tabl

%O 6,1

%A _Asher Auel_, Dec 12 1999

%E a(30) corrected by _T. D. Noe_, Feb 08 2008