|
|
|
|
0, 0, 0, 1, 5, 21, 81, 302, 1107, 4027, 14608, 52988, 192501, 701065, 2560806, 9384273, 34504203, 127288011, 471102318, 1749063906, 6513268401, 24323719461, 91081800417, 341929853235, 1286711419527, 4852902998951, 18341683253676
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Number of Dyck n-paths with at least one UUU. - David Scambler, Sep 17 2012
|
|
LINKS
|
|
|
FORMULA
|
Conjecture: -(n+1)*(n-3)*(n+2)^2*a(n) +3*(n+1)*(2*n^3-n^2-15*n+8)*a(n-1) -(n-1)*(5*n^3-41*n+48)*a(n-2) -6*(n-1)*(n-2)*(2*n-5)*(n+3)*a(n-3)=0, n>=6 - R. J. Mathar, Mar 04 2018
|
|
MAPLE
|
A001006 := proc(n) (3/2)^(n+2)*add( 3^(-k)*A000108(k-1)*binomial(k, n+2-k), k=1..n+2) ; end:
end:
|
|
MATHEMATICA
|
MotzkinNumber = DifferenceRoot[Function[{y, n}, {(-3n-3)*y[n] + (-2n-5)*y[n+1] + (n+4)*y[n+2] == 0, y[0] == 1, y[1] == 1}]];
a[n_] := CatalanNumber[n] - MotzkinNumber[n];
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|