A383480 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(4,0),(0,1).
1, 2, 6, 20, 75, 294, 1176, 4752, 19350, 79310, 326898, 1353768, 5628441, 23478700, 98217840, 411879264, 1730924700, 7287941340, 30736775190, 129825892000, 549096132585, 2325216522420, 9857299586700, 41830206233400, 177673556967075, 755307883986084, 3213402383779812
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..1564
Programs
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Maple
f:= proc(x,y) option remember; local t; t:= 0; if x >= 1 then t:= t + procname(x-1,y) fi; if x >= 4 then t:= t + procname(x-4,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..26); # Robert Israel, May 28 2025 -
PARI
a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-3*k, n-4*k));
Formula
a(n) = [x^n] 1/(1 - x - x^4)^(n+1).
a(n) = (n+1) * A063021(n+1).
a(n) = Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(2*n-3*k,n-4*k).