OFFSET
0,5
COMMENTS
T(n+1,k) = (T(n,k) + T(n,k-1)) mod 16. - Reinhard Zumkeller, Mar 14 2015
LINKS
Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened
Ilya Gutkovskiy, Illustrations (triangle formed by reading Pascal's triangle mod m)
James G. Huard, Blair K. Spearman, and Kenneth S. Williams, Pascal's triangle (mod 8), European Journal of Combinatorics 19:1 (1998), pp. 45-62.
FORMULA
T(i, j) = binomial(i, j) mod 16.
EXAMPLE
Triangle begins:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 4 15 6 1
1 7 5 3 3 5 7 1
1 8 12 8 6 8 12 8 1
1 9 4 4 14 14 4 4 9 1
1 10 13 8 2 12 2 8 13 10 1
1 11 7 5 10 14 14 10 5 7 11 1
.
Written in hexadecimal (with a=10, b=11, ..., f=15), rows 0..32 are
.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 a a 5 1
1 6 f 4 f 6 1
1 7 5 3 3 5 7 1
1 8 c 8 6 8 c 8 1
1 9 4 4 e e 4 4 9 1
1 a d 8 2 c 2 8 d a 1
1 b 7 5 a e e a 5 7 b 1
1 c 2 c f 8 c 8 f c 2 c 1
1 d e e b 7 4 4 7 b e e d 1
1 e b c 9 2 b 8 b 2 9 c b e 1
1 f 9 7 5 b d 3 3 d b 5 7 9 f 1
1 0 8 0 c 0 8 0 6 0 8 0 c 0 8 0 1
1 1 8 8 c c 8 8 6 6 8 8 c c 8 8 1 1
1 2 9 0 4 8 4 0 e c e 0 4 8 4 0 9 2 1
1 3 b 9 4 c c 4 e a a e 4 c c 4 9 b 3 1
1 4 e 4 d 0 8 0 2 8 4 8 2 0 8 0 d 4 e 4 1
1 5 2 2 1 d 8 8 2 a c c a 2 8 8 d 1 2 2 5 1
1 6 7 4 3 e 5 0 a c 6 8 6 c a 0 5 e 3 4 7 6 1
1 7 d b 7 1 3 5 a 6 2 e e 2 6 a 5 3 1 7 b d 7 1
1 8 4 8 2 8 4 8 f 0 8 0 c 0 8 0 f 8 4 8 2 8 4 8 1
1 9 c c a a c c 7 f 8 8 c c 8 8 f 7 c c a a c c 9 1
1 a 5 8 6 4 6 8 3 6 7 0 4 8 4 0 7 6 3 8 6 4 6 8 5 a 1
1 b f d e a a e b 9 d 7 4 c c 4 7 d 9 b e a a e d f b 1
1 c a c b 8 4 8 9 4 6 4 b 0 8 0 b 4 6 4 9 8 4 8 b c a c 1
1 d 6 6 7 3 c c 1 d a a f b 8 8 b f a a d 1 c c 3 7 6 6 d 1
1 e 3 c d a f 8 d e 7 4 9 a 3 0 3 a 9 4 7 e d 8 f a d c 3 e 1
1 f 1 f 9 7 9 7 5 b 5 b d 3 d 3 3 d 3 d b 5 b 5 7 9 7 9 f 1 f 1
1 0 0 0 8 0 0 0 c 0 0 0 8 0 0 0 6 0 0 0 8 0 0 0 c 0 0 0 8 0 0 0 1
MATHEMATICA
Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 16] (* Robert G. Wilson v, May 26 2004 *)
PROG
(Haskell)
a034932 n k = a034932_tabl !! n !! k
a034932_row n = a034932_tabl !! n
a034932_tabl = iterate
(\ws -> zipWith ((flip mod 16 .) . (+)) ([0] ++ ws) (ws ++ [0])) [1]
-- Reinhard Zumkeller, Mar 14 2015
CROSSREFS
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), A034930 (m = 8), A095143 (m = 9), A008975 (m = 10), A095144 (m = 11), A095145 (m = 12), A275198 (m = 14), (this sequence) (m = 16).
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved