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A231642
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Triangle read by rows, t(n,k) = binomial(n,k) mod n, k <= n.
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1
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0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 3, 2, 3, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 6, 0, 4, 0, 1, 0, 0, 3, 0, 0, 3, 0, 0, 1, 0, 5, 0, 0, 2, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 4, 3, 0, 0, 0, 3, 4, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 7, 0, 7, 0, 7, 2, 7, 0, 7, 0, 7, 0, 1
(list;
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refs;
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history;
text;
internal format)
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OFFSET
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1,8
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COMMENTS
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Rows of the form 0,0,0,...,0,1 fit prime n.
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LINKS
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T. D. Noe, Rows n = 1..100 of triangle, flattened
Frank Ruskey, Carla D. Savage, and Stan Wagon, The Search for Simple Symmetric Venn Diagrams, page 1.
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EXAMPLE
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Triangle begins:
0;
0, 1;
0, 0, 1;
0, 2, 0, 1;
0, 0, 0, 0, 1;
0, 3, 2, 3, 0, 1;
0, 0, 0, 0, 0, 0, 1;
etc.
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MATHEMATICA
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t[n_, k_] := Mod[Binomial[n, k], n]; Table[t[n, k], {n, 14}, {k, n}] // Flatten
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PROG
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(PARI) t(n, k)=binomial(n, k)%n \\ Charles R Greathouse IV, Nov 12 2013
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CROSSREFS
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Sequence in context: A113048 A331671 A123758 * A288318 A219483 A239927
Adjacent sequences: A231639 A231640 A231641 * A231643 A231644 A231645
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KEYWORD
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nonn,tabl
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AUTHOR
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Jean-François Alcover, Nov 12 2013
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STATUS
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approved
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