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%I #14 Feb 20 2024 03:28:14
%S 0,1,8,26,63,124,208,335,504,702,973,1304,1664,2133,2680,3250,3971,
%T 4788,5616,6643,7784,8918,10305,11824,13312,15113,17064,18954,21223,
%U 23660,26000,28791,31768,34606,37973,41544,44928,48925,53144,57122
%N a(n) = n^3 - floor(n/3)^3.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,-3,0,-3,3,0,1,-1).
%F a(n) = a(n-1)+3*a(n-3)-3*a(n-4)-3*a(n-6)+3*a(n-7)+a(n-9)-a(n-10).
%F G.f.: (x^2 + 7*x^3 + 18*x^4 + 34*x^5 + 40*x^6 + 30*x^7 + 19*x^8 + 7*x^9)/(1 - x - 3*x^3 + 3*x^4 + 3*x^6 - 3*x^7 - x^9 + x^10).
%t a[n_] := n^3 - Floor[n/3]^3
%t Table[a[n], {n, 0, 90}] (* A213039 *)
%t LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {0, 1, 8, 26, 63, 124, 208, 335, 504, 702}, 90]
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Jun 06 2012