A034930 - OEIS

%I #27 Dec 17 2021 01:42:53

%S 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,2,2,5,1,1,6,7,4,7,6,1,1,7,5,3,3,5,

%T 7,1,1,0,4,0,6,0,4,0,1,1,1,4,4,6,6,4,4,1,1,1,2,5,0,2,4,2,0,5,2,1,1,3,

%U 7,5,2,6,6,2,5,7,3,1,1,4,2,4,7,0,4,0,7,4,2,4,1,1,5,6,6,3,7,4,4,7,3,6,6,5,1

%N Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 8.

%H Reinhard Zumkeller, <a href="/A034930/b034930.txt">Rows n = 0..120 of triangle, flattened</a>

%H Ilya Gutkovskiy, <a href="/A275198/a275198.pdf">Illustrations (triangle formed by reading Pascal's triangle mod m)</a>

%H James G. Huard, Blair K. Spearman, and Kenneth S. Williams, <a href="https://doi.org/10.1006/eujc.1997.0146">Pascal's triangle (mod 8)</a>, European Journal of Combinatorics 19:1 (1998), pp. 45-62.

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%F T(n+1,k) = (T(n,k) + T(n,k-1)) mod 8. - _Reinhard Zumkeller_, Jul 12 2013

%t Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 8] (* _Robert G. Wilson v_, May 26 2004 *)

%o (Haskell)

%o a034930 n k = a034930_tabl !! n !! k

%o a034930_row n = a034930_tabl !! n

%o a034930_tabl = iterate

%o    (\ws -> zipWith (\u v -> mod (u + v) 8) ([0] ++ ws) (ws ++ [0])) [1]

%o -- _Reinhard Zumkeller_, Jul 12 2013, Jun 21 2013

%Y Cf. A007318, A047999, A083093, A034931, A008975, A034932.

%Y Sequences based on the triangles formed by reading Pascal's triangle mod m: A047999 (m = 2), A083093 (m = 3), A034931 (m = 4), A095140 (m = 5), A095141 (m = 6), A095142 (m = 7), (this sequence) (m = 8), A095143 (m = 9), A008975 (m = 10), A095144 (m = 11), A095145 (m = 12), A275198 (m = 14), A034932 (m = 16).

%K nonn,tabl

%O 0,5

%A _N. J. A. Sloane_