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A079280 Number of log-concave paths of length n starting from the origin (0,0) with steps from {N=(0,1), E=(1,0) and S=(0,-1)} that stay in the second octant and never touch the line y=x except possibly at the beginning or the end. 0
1, 2, 2, 5, 7, 17, 26, 62, 99, 233, 382, 890, 1486, 3434, 5812, 13340, 22819, 52073, 89846, 204002, 354522, 801422, 1401292, 3155300, 5546382, 12444842, 21977516, 49155332, 87167164, 194392628, 345994216, 769547192, 1374282019, 3049104233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The first S step can only come after an E step.

LINKS

Table of n, a(n) for n=1..34.

FORMULA

G.f.: (1-x)/(2-4*x) + (1+3*x)/(2*sqrt(1-4*x^2));

a(2n) = (1/2)*(4^(n-1) + 3*binomial(2n-2, n-1));

a(2n+1) = (1/2)*(2*4^(n-1) + binomial(2n, n)).

CROSSREFS

Sequence in context: A127413 A145344 A034438 * A038750 A300439 A208818

Adjacent sequences:  A079277 A079278 A079279 * A079281 A079282 A079283

KEYWORD

nonn,changed

AUTHOR

Wenjin Woan, Feb 07 2003

EXTENSIONS

More terms from Max Alekseyev, Jul 04 2009

STATUS

approved

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)