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Search: id:A131268
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| A131268 |
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Triangle read by rows: T(n,k)=2* binomial(n-floor((k+1)/2),floor(k/2))-1 (0<=k<=n). |
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+0
3
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| 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 3, 1, 1, 1, 7, 5, 5, 1, 1, 1, 9, 7, 11, 5, 1, 1, 1, 11, 9, 19, 11, 7, 1, 1, 1, 13, 11, 29, 19, 19, 7, 1, 1, 1, 15, 13, 41, 29, 39, 19, 9, 1, 1, 1, 17, 15, 55, 41, 69, 39, 29, 9, 1, 1, 1, 19, 17, 71, 55, 111, 69, 69, 29, 11, 1, 1, 1, 21, 19, 89, 71, 167
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Row sums = A131269: (1, 2, 3, 6, 11, 20, 35,...). Reversal = triangle A131270.
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FORMULA
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2*A065941 - A000012, where A065941 = Pascal's triangle with repeated columns; and A000012 = (1; 1,1; 1,1,1;...) as an infinite lower triangular matrix.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 1, 1;
1, 1, 3, 1;
1, 1, 5, 3, 1;
1, 1, 7, 5, 5, 1;
1, 1, 9, 7, 11, 5, 1;
1, 1, 11, 9, 19, 11, 7, 1;
...
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MAPLE
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T := proc (n, k) options operator, arrow; 2*binomial(n-floor((1/2)*k+1/2), floor((1/2)*k))-1 end proc: for n from 0 to 12 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2007
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CROSSREFS
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Cf. A065941, A000012, A131269, A131270.
Sequence in context: A028234 A052125 A081060 this_sequence A109221 A046643 A112475
Adjacent sequences: A131265 A131266 A131267 this_sequence A131269 A131270 A131271
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 23 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 15 2007
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