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A034932
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Triangle, read by rows, formed by reading Pascal's triangle (A007318) mod 16.
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15
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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)
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OFFSET
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0,5
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COMMENTS
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LINKS
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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.
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FORMULA
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T(i, j) = binomial(i, j) mod 16.
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EXAMPLE
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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
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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
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MATHEMATICA
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Mod[ Flatten[ Table[ Binomial[n, k], {n, 0, 13}, {k, 0, n}]], 16] (* Robert G. Wilson v, May 26 2004 *)
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PROG
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(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]
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CROSSREFS
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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).
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KEYWORD
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AUTHOR
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STATUS
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approved
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