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Search: id:A090345
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| A090345 |
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Number of Motzkin paths of length n with no level steps at even level. |
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+0
2
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| 1, 0, 1, 1, 3, 5, 12, 24, 55, 119, 272, 612, 1411, 3247, 7565, 17667, 41561, 98099, 232696, 553784, 1322813, 3169065, 7614583, 18342921, 44294991, 107200829, 259983346, 631718606, 1537737567, 3749440151, 9156561590, 22394270034
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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G.f.=[1-z-sqrt(1-2z-3z^2+4z^3)]/(2z^2).
G.f. A(x) satisfies A(x)=A(x/(x-1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 07 2004
Also (x*A)^2=(1-x)*(A-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 07 2004
G.f.: 1/(1-x^2/(1-x-x^2/(1-x^2/(1-x-x^2/(1-x^2/(1-x-x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 08 2009]
a(0)=1, a(n)=sum{k=0..floor(n/2), (k/(n-k))C(n-k,k)*A000108(k)}. [From Paul Barry (pbarry(AT)wit.ie), Jul 01 2009]
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EXAMPLE
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a(5)=5 because we have UHDUD, UDUHD, UHUDD, UUDHD and UHHHD, where U=(1,1),
D=(1,-1) and H=(1,0).
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CROSSREFS
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Cf. A001006.
First differences of A090344.
Sequence in context: A047761 A026786 A027246 this_sequence A151524 A030270 A129757
Adjacent sequences: A090342 A090343 A090344 this_sequence A090346 A090347 A090348
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 28 2004
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