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Search: id:A131238
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| A131238 |
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Triangle read by rows: T(n,k)=2binom(n,k) - binom(floor(n/2+k/2),k) (0<=k<=n). |
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2
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| 1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 6, 9, 7, 1, 1, 7, 17, 16, 9, 1, 1, 9, 24, 36, 25, 11, 1, 1, 10, 36, 60, 65, 36, 13, 1, 1, 12, 46, 102, 125, 106, 49, 15, 1, 1, 13, 62, 148, 237, 231, 161, 64, 17, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums = A027934: (1, 2, 5, 11, 24, 51, 107,...). A131239 = 3*A007318 - 2*A046854.
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FORMULA
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2*A007318 - A046854 as infinite lower triangular matrices, where A007318 = Pascal's triangle and A046854 = Pascal's triangle with repeats, by columns.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 4, 5, 1;
1, 6, 9, 7, 1;
1, 7, 17, 16, 9, 1;
1, 9, 24, 36, 25, 11, 1;
1, 10, 36, 60, 65, 36, 13, 1;
...
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MAPLE
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T := proc (n, k) options operator, arrow; 2*binomial(n, k)-binomial(floor((1/2)*n+(1/2)*k), k) end proc: for n from 0 to 9 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 09 2007
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CROSSREFS
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Cf. A027934, A131239, A007318, A046854.
Adjacent sequences: A131235 A131236 A131237 this_sequence A131239 A131240 A131241
Sequence in context: A124234 A135226 A104730 this_sequence A133380 A105687 A058879
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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 21 2007
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