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1, 3, 10, 33, 110, 366, 1220, 4065, 13550, 45162, 150540, 501786, 1672620, 5575356, 18584520, 61948257, 206494190, 688313490, 2294378300, 7647926046, 25493086820, 84976950468, 283256501560, 944188318938, 3147294396460
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is A000012=[1,1,1,1,1,1,1,...].
a(n) is the number of Motzkin paths of length n in which the (1,0)-steps at level 0 come in 3 colors and there are no (1,0)-steps at a higher level. Example: a(3)=33 because, denoting U=(1,1), H=(1,0), and D=(1,-1), we have 3^3 = 27 paths of shape HHH, 3 paths of shape HUD, and 3 paths of shape UDH. - Emeric Deutsch, May 02 2011
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FORMULA
| G.f.: 1/(1-3x-x^2/(1-x^2/(1-x^2/(1-x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Mar 10 2009]
G.f. = 2/[1-6z+sqrt(1-4z^2)]. - Emeric Deutsch, May 02 2011
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MAPLE
| A127359 := proc(n) add(binomial(n, floor(k/2))*3^(n-k), k=0..n) ; end proc: A126931 := proc(n) A127359(n+1)/2-A127359(n) ; end proc: seq(A126931(n), n=0..50) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 25 2010]
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CROSSREFS
| Sequence in context: A006190 A020704 A113299 * A071722 A058987 A001558
Adjacent sequences: A126928 A126929 A126930 * A126932 A126933 A126934
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 17 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 25 2010
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