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A080937 Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2n steps with all values less than or equal to 5. +0
9
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)
OFFSET

0,3

COMMENT

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

FORMULA

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

CROSSREFS

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: A148327 A092493 A148328 this_sequence A054392 A006930 A036767

Adjacent sequences: A080934 A080935 A080936 this_sequence A080938 A080939 A080940

KEYWORD

nonn

AUTHOR

Henry Bottomley (se16(AT)btinternet.com), Feb 25 2003

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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