OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 3/4*(71 + 8*sqrt(2))^(1/3) + 51/(4*(71 + 8*sqrt(2))^(1/3)) + 13/4 = 9.4435356015932520820011..., c = 0.00814413508604516738631686716788556507884786... . - Vaclav Kotesovec, Sep 07 2014
EXAMPLE
a(2) = 2: UDSS, UU.
a(3) = 7: UDSDSSS, UDUSS, UDSSDSS, UUDSS, UDSUS, UDSSU, UUU.
MAPLE
b:= proc(x, y) option remember; `if`(y>x, 0, `if`(x=0, 1,
`if`(y>0, b(x, y-1)+b(x-1, y-1), 0)+b(x-1, y+1)))
end:
a:= n-> b(n, n):
seq(a(n), n=0..30);
MATHEMATICA
b[x_, y_] := b[x, y] = If[y > x, 0, If[x == 0, 1, If[y > 0, b[x, y - 1] + b[x - 1, y - 1], 0] + b[x - 1, y + 1]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 17 2013
STATUS
approved