OFFSET
0,2
COMMENTS
For n > 0, a(n)-1 is the sum of the n-th row of Motzkin's triangle (A026300). - Daniel Suteu, Feb 23 2018
FORMULA
Recurrence: {a(3) = 14, a(4) = 36, a(1) = 3, a(2) = 6, a(0) = 1, (-3-3*n)*a(n)+(-6-2*n)*a(1+n)+(3+n)*a(n+2)+6+4*n}.
G.f.: ((1/2)*i)*sqrt(t+1)/(t*sqrt(3*t-1))-(1/2)*(t+1)*(-1+2*t)/((t-1)*t).
a(n) = 1 + Sum_{k=0..n} Sum_{t=0..floor(k/2)} binomial(n, 2*t + n - k) * (binomial(2*t + n - k, t) - binomial(2*t + n - k, t-1)), for n > 0. - Daniel Suteu, Feb 23 2018
EXAMPLE
a(1) = 3 because all three directions are permissible from the origin;
a(2) = 6 because all three directions are permissible following the southwestern step and the southwest as well as southeast steps are permissible following the southeastern step, but only the eastern step is permissible following one step east.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Rebecca Xiaoxi Nie (rebecca.nie(AT)utoronto.ca), Jun 01 2007
STATUS
approved