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A383478
Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(3,0),(0,1).
2
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
0,2
LINKS
FORMULA
a(n) = [x^n] 1/(1 - x - x^2 - x^3)^(n+1).
a(n) = (n+1) * A063018(n+1).
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
CROSSREFS
Main diagonal of A383477.
Cf. A063018.
Sequence in context: A216861 A390528 A199308 * A387677 A176479 A162356
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 28 2025
STATUS
approved