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Search: id:A124732
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| A124732 |
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Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,...) in the main diagonal and (2,1,2,1,...) in the subdiagonal. |
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+0
3
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| 1, 3, 2, 5, 5, 1, 7, 9, 5, 2, 9, 14, 14, 9, 1, 11, 20, 30, 25, 7, 2, 13, 27, 55, 55, 27, 13, 1, 15, 35, 91, 105, 77, 49, 9, 2, 17, 44, 140, 182, 182, 140, 44, 17, 1, 19, 54, 204, 294, 378, 336, 156, 81, 11, 2, 21, 65, 285, 450, 714, 714, 450, 285, 65, 21, 1, 23, 77, 385, 660
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums = A052940: (1, 5, 11, 23, 47, 95...).
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FORMULA
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T(n,k)=binom(n,k)[3n-(-1)^k*(n-2*k)]/(2n) (1<=k<=n).
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EXAMPLE
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First 3 rows of the triangle are (1; 3,2; 5,5,1) since [1,0,0; 1,1,0; 1,2,1] * [1,0,0; 2,2,0; 0,1,1] = [1,0,0; 3,2,0; 5,5,1].
First few rows of the triangle are:
1;
3, 2;
5, 5, 1;
7, 9, 5, 2;
9, 14, 14, 9, 1;
11, 20, 30, 25, 7, 2;
13, 27, 55, 55, 27, 13, 1;
15, 35, 91, 105, 77, 49, 9, 2;
...
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MAPLE
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T:=(n, k)->binomial(n, k)*(3*n-(-1)^k*(n-2*k))/2/n: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A124730, A052940.
Sequence in context: A054080 A120332 A095006 this_sequence A094787 A132778 A127703
Adjacent sequences: A124729 A124730 A124731 this_sequence A124733 A124734 A124735
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 05 2006
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EXTENSIONS
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Edited by njas, Nov 24 2006
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