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A268214 Number of paths from (0,0) to (n,n) that use E(1,0) and N(0,1) as steps and have odd number of East steps below the line y=x-1. 1
0, 0, 1, 4, 19, 72, 302, 1144, 4643, 17680, 70874, 271320, 1081742, 4160240, 16543932, 63871920, 253681955, 982571040, 3900295586, 15147970200, 60117323162, 234025162800, 928766304388, 3622709520144, 14378870714254, 56182491750112, 223031678941252 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.
FORMULA
a(n) = binomial(2*n,n) - A268213(n).
G.f.: (8*x^2*g(x)-(f(x)-1)*(g(x)+1)+2*x*(-2+f(x)-3*g(x)+2*f(x)*g(x))) / (16*x^2*(4*x-1)), where f(x) = sqrt(1-4*x) and g(x) = sqrt(1+4*x).
PROG
(PARI) x='x+O('x^50); f=sqrt(1-4*x); g=sqrt(1+4*x); concat([0, 0], Vec((8*x^2*g-(f-1)*(g+1)-2*x*(2-f+3*g-2*f*g))/(16*x^4*(4*x-1)))) \\ Charles R Greathouse IV, Feb 01 2016
CROSSREFS
Sequence in context: A267192 A219972 A284224 * A027208 A085348 A027232
KEYWORD
nonn
AUTHOR
Ran Pan, Jan 28 2016
STATUS
approved

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Last modified April 13 07:58 EDT 2024. Contains 371638 sequences. (Running on oeis4.)