A227666 Number of lattice paths from {n}^4 to {0}^4 using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_4) we have abs(p_{i}-p_{i+1}) <= 1.

1, 24, 896, 33904, 1281696, 48447504, 1831288096, 69221669104, 2616540574496, 98903777810704, 3738507768500896, 141313513441272304, 5341572177372667296, 201908456107703653904, 7632027293479058673696, 288486385024598708555504, 10904624832208006924120096

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (40,-89,220).

Formula

G.f.: (20*x^3-25*x^2+16*x-1)/(220*x^3-89*x^2+40*x-1).

a(n) = 40*a(n-1) -89*a(n-2) +220*a(n-3) for n>3, a(0)=1, a(1)=24, a(2)=896, a(3)=33904.

Example

a(1) = 4! = 24.

Maple

a:= n-> ceil((<<0|1|0>, <0|0|1>, <220|-89|40>>^n.
        <<10/11, 24, 896>>)[1, 1]):
seq(a(n), n=0..25);

Crossrefs

Column k=4 of A227655.

Cf. A000142.

Sequence in context: A246215 A109575 A160111 * A107391 A281778 A006147

Adjacent sequences: A227663 A227664 A227665 * A227667 A227668 A227669

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 19 2013

Status

approved