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Search: id:A080937
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| A080937 |
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Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2n steps with all values less than or equal to 5. |
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+0
9
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| 1, 1, 2, 5, 14, 42, 131, 417, 1341, 4334, 14041, 45542, 147798, 479779, 1557649, 5057369, 16420730, 53317085, 173118414, 562110290, 1825158051, 5926246929, 19242396629, 62479659622, 202870165265, 658715265222, 2138834994142
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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With interpolated zeros (1,0,1,0,2,...), counts closed walks of length n at start or end node of P_6. The sequence (0,1,0,2,...) counts walks of length n between the start and second node. - Paul Barry (pbarry(AT)wit.ie), Jan 26 2005
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FORMULA
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a(n) =A080934(n, 5)
G.f.: (1-4x+3x^2)/(1-5x+6x^2-x^3). - Ralf Stephan (ralf(AT)ark.in-berlin.de), May 13 2003
a(n) = 5a(n-1)-6a(n-2)+a(n-3) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 11 2004
a(n)=A096976(2n) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Nov 02 2005
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CROSSREFS
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Cf. A000007, A000012, A011782, A001519, A007051, A080937, A024175, A080938, A033191 which essentially provide the same sequence for different limits, and tend to A000108.
Cf. A094790, A094789, A005021.
Sequence in context: A025274 A132833 A092493 this_sequence A054392 A006930 A036767
Adjacent sequences: A080934 A080935 A080936 this_sequence A080938 A080939 A080940
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Feb 25 2003
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