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Search: id:A108891
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| A108891 |
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Triangle read by rows: T(n,k) = number of Schroeder (or royal) n-paths (A006318) containing k returns to the diagonal y=x. (A northeast step lying on y=x contributes a return.) |
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1
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| 2, 2, 4, 6, 8, 8, 22, 28, 24, 16, 90, 112, 96, 64, 32, 394, 484, 416, 288, 160, 64, 1806, 2200, 1896, 1344, 800, 384, 8558, 10364, 8952, 6448, 4000, 2112, 41586, 50144, 43392, 31616, 20160, 11264
(list; table; graph; listen)
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OFFSET
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1,1
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FORMULA
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Column k is the k-fold convolution of column 1.
T(n, k) = A104219(n-1, k-1)*2^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 31 2005
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EXAMPLE
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Table begins
\ k..1....2....3....4....5....6
n\
1 |..2
2 |..2....4
3 |..6....8....8
4 |.22...28...24...16
5 |.90..112...96...64...32
6 |394..484..416..288..160...64
The paths DD, END, DEN, ENEN each have 2 returns (E=east, N=north, D=northeast); so T(2,2)=4.
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CROSSREFS
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Row sums are the large Schroeder numbers A006318. Column k=1 is twice the little Schroeder numbers A001003. The main diagonal consists of powers of 2, A000079. The first subdiagonal is A036289. The analogous Catalan triangle is A009766 (with rows reversed).
Sequence in context: A046639 A089284 A081488 this_sequence A147570 A049625 A118303
Adjacent sequences: A108888 A108889 A108890 this_sequence A108892 A108893 A108894
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KEYWORD
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nonn,tabl
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AUTHOR
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David Callan (callan(AT)stat.wisc.edu), Jul 25 2005
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