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

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..1564

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).

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

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(2*n-3*k, n-4*k));

Crossrefs

Cf. A038112, A383479.

Cf. A063021, A383481.

Sequence in context: A150164 A150165 A148482 * A148483 A150166 A150167

Adjacent sequences: A383477 A383478 A383479 * A383481 A383482 A383483

Keyword

nonn

Author

Seiichi Manyama, Apr 28 2025

Status

approved