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Search: id:A026003
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| A026003 |
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a(n) = T([n/2],[(n+1)/2]), where T = Delannoy triangle (A008288). |
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+0
7
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| 1, 1, 3, 5, 13, 25, 63, 129, 321, 681, 1683, 3653, 8989, 19825, 48639, 108545, 265729, 598417, 1462563, 3317445, 8097453, 18474633, 45046719, 103274625, 251595969, 579168825, 1409933619, 3256957317, 7923848253, 18359266785, 44642381823
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of lattice paths from (0,0) to the line x=n consisting of U=(1,1), D=(1,-1), and H=(2,0) steps and never going below the x-axis (i.e. left factors of Schroeder paths); for example, a(3)=5, counting the paths UUU,UUD,UDU,HU, and UH. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 27 2002
Transform of A001405 by |A049310(n,k)|, that is, transform of central binomial coefficients C(n,floor(n/2)) by Chebyshev mapping which takes a sequence with g.f. g(x) to the sequence with g.f. (1/(1-x^2))g(x/(1-x^2)). - Paul Barry (pbarry(AT)wit.ie), Jul 30 2005
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FORMULA
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G.f.: (sqrt((x^2-2*x-1)/(x^2+2*x-1))-1)/2/x. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 27 2003
a(n)=sum{k=0..floor(n/2), C(n-k, k)C(n-2k, floor((n-2k)/2))}. - Paul Barry (pbarry(AT)wit.ie), Jul 30 2005
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CROSSREFS
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Bisections are Delannoy numbers (A001850) and A002002.
Sequence in context: A110494 A098615 A026720 this_sequence A103792 A076156 A084173
Adjacent sequences: A026000 A026001 A026002 this_sequence A026004 A026005 A026006
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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