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
Examples
a(1) = 4! = 24.
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).
Programs
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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);
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.