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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.

%I A227666 #11 Jun 13 2015 00:54:42
%S A227666 1,24,896,33904,1281696,48447504,1831288096,69221669104,2616540574496,
%T A227666 98903777810704,3738507768500896,141313513441272304,
%U A227666 5341572177372667296,201908456107703653904,7632027293479058673696,288486385024598708555504,10904624832208006924120096
%N 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.
%H A227666 Alois P. Heinz, <a href="/A227666/b227666.txt">Table of n, a(n) for n = 0..500</a>
%H A227666 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (40,-89,220).
%F A227666 G.f.: (20*x^3-25*x^2+16*x-1)/(220*x^3-89*x^2+40*x-1).
%F A227666 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.
%e A227666 a(1) = 4! = 24.
%p A227666 a:= n-> ceil((<<0|1|0>, <0|0|1>, <220|-89|40>>^n.
%p A227666         <<10/11, 24, 896>>)[1, 1]):
%p A227666 seq(a(n), n=0..25);
%Y A227666 Column k=4 of A227655.
%Y A227666 Cf. A000142.
%K A227666 nonn,easy
%O A227666 0,2
%A A227666 _Alois P. Heinz_, Jul 19 2013