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Search: id:A099172
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| A099172 |
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Array T(m,n) read by antidiagonals: binary strings with m 1's and n 0's without zigzags. |
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+0
2
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| 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 2, 5, 5, 2, 1, 1, 2, 6, 8, 6, 2, 1, 1, 2, 7, 11, 11, 7, 2, 1, 1, 2, 8, 14, 18, 14, 8, 2, 1, 1, 2, 9, 17, 26, 26, 17, 9, 2, 1, 1, 2, 10, 20, 35, 42, 35, 20, 10, 2, 1, 1, 2, 11, 23, 45, 62, 62, 45, 23, 11, 2, 1, 1, 2, 12, 26, 56, 86, 100, 86
(list; table; graph; listen)
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OFFSET
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0,5
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LINKS
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E. Munarini and N. Z. Salvi, Binary strings without zigzags
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FORMULA
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G.f.: (1 + xy + x^2y^2)/(1 - x - y + xy - x^2y^2).
T(m, n) = Sum{k=0..min(m+[m/2], n+[n/2]), C(m-k+2[k/3], [k/3])*C(n-k+2[k/3], [k/3]) }.
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EXAMPLE
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1,1,1,1,1,1,1,1,
1,2,2,2,2,2,2,2,
1,2,4,5,6,7,8,9,
1,2,5,8,11,14,17,20,
1,2,6,11,18,26,35,45,
1,2,7,14,26,42,62,86,
1,2,8,17,35,62,100,150,
1,2,9,20,45,86,150,242,
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PROGRAM
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(PARI) T(m, n)=sum(k=0, min(m+m\2, n+n\2), binomial(m-k+2*(k\3), k\3)*binomial(n-k+2*(k\3), k\3))
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CROSSREFS
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Main diagonal is A078678. Antidiagonal sums are essentially A006355.
Sequence in context: A144464 A138015 A103444 this_sequence A152719 A107044 A141591
Adjacent sequences: A099169 A099170 A099171 this_sequence A099173 A099174 A099175
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Oct 10 2004
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