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A186648 Number of walks f length n on a square lattice ending with x > 0 and y > 0. 1
0, 0, 2, 6, 38, 130, 662, 2380, 11174, 41226, 185642, 695860, 3055670, 11576916, 49995220, 190876696, 814610854, 3128164186, 13233277634, 51046844836, 214488337418, 830382690556, 3470405605900, 13475470680616, 56073057254198, 218269673491780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

E.g.f.: ((e^(2*x)-I_0(2*x))/2)^2. - Benjamin Phillabaum, Mar 06 2011

From Benedict W. J. Irwin, May 25 2016: (Start)

If n is even, a(n) = 2^(n-2)*(2^n - 2*2F1((1-n)/2,-n/2;1;1) + n!*Gamma((n+1)/2))/(sqrt(Pi)*Gamma(1 + n/2)^3),

If n is odd, a(n) = 2^(n-2)*(2^n - 2*2F1((1-n)/2,-n/2;1;1)).

(End)

EXAMPLE

a(3) = 6 {UUR,URU,RUU,RRU,RUR,URR}. Note: you can also go Left or Down, however that appears at the fourth sequence which is too large to put in this space.

MATHEMATICA

Table[(CoefficientList[Series[(1/2 (E^(2 x) - (BesselI[0, 2 x])))^2, {x, 0, len}], x] Range[0, len]!)[[n + 1]], {n, 0, 25}]

CROSSREFS

Cf. A187151.

Sequence in context: A117266 A259437 A202737 * A013033 A233130 A267405

Adjacent sequences:  A186645 A186646 A186647 * A186649 A186650 A186651

KEYWORD

nonn,walk

AUTHOR

Benjamin Phillabaum, Mar 06 2011

STATUS

approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)