A383478 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(3,0),(0,1).

1, 2, 9, 44, 220, 1134, 5950, 31608, 169488, 915420, 4972825, 27141036, 148711836, 817516196, 4506838380, 24906188912, 137933068572, 765324011736, 4253501563156, 23675286219200, 131955035141160, 736347621539310, 4113559552360230, 23003228298637080

Offset: 0

Author

Seiichi Manyama, Apr 28 2025

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..1316

Crossrefs

Main diagonal of A383477.

Cf. A063018.

Programs

Maple

f:= proc(x,y) option remember;
     local t;
     t:= 0;
     if x >= 1 then t:= t + procname(x-1,y) fi;
     if x >= 2 then t:= t + procname(x-2,y) fi;
     if x >= 3 then t:= t + procname(x-3,y) fi;
     if y >= 1 then t:= t + procname(x,y-1) fi;
     t
end proc:
f(0,0):= 1:
seq(f(n,n),n=0..25); # Robert Israel, May 28 2025

Formula

a(n) = [x^n] 1/(1 - x - x^2 - x^3)^(n+1).

a(n) = (n+1) * A063018(n+1).