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 A034932 Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 16. 15
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 Cf. A007318, A047999, A083093, A034931, A034930, A008975. 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). Sequence in context: A095144 A339359 A144398 * A180183 A273914 A094495 Adjacent sequences:  A034929 A034930 A034931 * A034933 A034934 A034935 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified August 8 10:26 EDT 2022. Contains 356009 sequences. (Running on oeis4.)