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%I #9 Apr 29 2022 18:35:30
%S 0,4,52,243,736,1750,3564,6517,11008,17496,26500,38599,54432,74698,
%T 100156,131625,169984,216172,271188,336091,412000,500094,601612,
%U 717853,850176,1000000,1168804,1358127,1569568,1804786,2065500,2353489,2670592,3018708,3399796
%N a(n) = n^3*(5*n+3)/2.
%C Number of ascending runs in {1,...,n}^4.
%H Alois P. Heinz, <a href="/A229146/b229146.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F G.f.: -(x^3+23*x^2+32*x+4)*x/(x-1)^5.
%p a:= n-> n^3*(5*n+3)/2:
%p seq(a(n), n=0..40);
%t Table[n^3(5n+3)/2,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,4,52,243,736},40] (* _Harvey P. Dale_, Apr 29 2022 *)
%Y Row n=4 of A229079.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Sep 15 2013