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Search: id:A064641
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| A064641 |
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Unidirectional 'Delannoy' variation of the Boustrophedon transform applied to all 1's sequence: in an array let the first element of each row be equal to 1 and find each next entry by T(n,k) = T(n,k-1) + T(n-1,k-1) + T(n-1,k) + T(n-2,k-1). The final number of row n gives a(n). |
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6
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| 1, 2, 7, 29, 133, 650, 3319, 17498, 94525, 520508, 2910895, 16487795, 94393105, 545337200, 3175320607, 18615098837, 109783526821, 650884962908, 3877184797783, 23193307022861, 139271612505361, 839192166392276
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also the number of paths from (0,0) to (n,n) not rising above y=x, using steps (1,0), (0,1), (1,1) and (2,1). For example, the 7 paths to (2,2) are dd, den, end, enen, Dn, eenn and edn, where e=(1,0), n=(0,1), d=(1,1) and D=(2,1). - Brian Drake (bdrake(AT)brandeis.edu), Aug 01 2007
Hankel transform is 3^C(n+1,2). [From Paul Barry (pbarry(AT)wit.ie), Jan 26 2009]
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LINKS
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Index entries for sequences related to boustrophedon transform
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FORMULA
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Generating function: (1-x-sqrt(1-6x-3x^2)) / (2x(1+x)) - Brian Drake (bdrake(AT)brandeis.edu), Aug 01 2007
G.f.: 1/(1-2x-3x^2/(1-3x-3x^2/(1-3x-3x^2/(1-3x-3x^2/(1-.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 26 2009]
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EXAMPLE
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The array begins
......1
....1...2
..1...5...7
1...8...22..29
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MAPLE
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A:= series( (1-x-sqrt(1-6*x-3*x^2)) / (2*x*(1+x)), x, 21): seq(coeff(A, x, i), i=0..20); - Brian Drake (bdrake(AT)brandeis.edu), Aug 01 2007
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x(1-x)/(1+x+x^2)+O(x^(n+2))), n+1)) (Paul Barry)
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CROSSREFS
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Delannoy numbers: A008288, table: A064642. Cf. A038764.
Sequence in context: A007852 A110576 A074600 this_sequence A104252 A018977 A030849
Adjacent sequences: A064638 A064639 A064640 this_sequence A064642 A064643 A064644
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KEYWORD
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nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 03 2001
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