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 A114296 First row of Modified Schroeder numbers for q=3 (A114292). 4
 1, 1, 2, 5, 16, 57, 224, 934, 4092, 18581, 86888, 415856, 2029160, 10061161, 50568680, 257129888, 1320619176, 6842177174, 35722456976, 187772944964, 992991472328, 5279633960181, 28208037066528, 151373637844440, 815568695756496, 4410124252008112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(i) is the number of paths from (0,0) to (i,i) using steps of length (0,1), (1,0) and (1,1), not passing above the line y=x nor below the line y=x/2. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 C. Hanusa, A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows, PhD Thesis, 2005, University of Washington, Seattle, USA. FORMULA a(n) ~ c * (3+2*sqrt(2))^n / n^(3/2), where c = 0.02741316010407391604887680145773... . - Vaclav Kotesovec, Sep 07 2014 EXAMPLE The number of paths from (0,0) to (3,3) staying between the lines y=x and y=x/2 using steps of length (0,1), (1,0) and (1,1) is a(3)=5. MAPLE b:= proc(x, y) option remember; `if`(y>x or y b(n, n): seq(a(n), n=0..30);  # Alois P. Heinz, Apr 25 2013 MATHEMATICA b[x_, y_] := b[x, y] = If[y>x || y

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Last modified August 21 18:38 EDT 2019. Contains 326168 sequences. (Running on oeis4.)