%I #14 Jun 09 2024 14:29:57

%S 0,0,0,0,0,4,12,28,57,104,173,273,409,591,828,1129,1506,1969,2532,

%T 3207,4009,4953,6053,7328,8793,10468,12372,14524,16944,19656,22680,

%U 26040,29760,33864,38380,43332,48748

%N [ n(n-1)(n-2)(n-3)/29 ].

%H <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 6, -4, 1).

%F From _Chai Wah Wu_, Aug 02 2020: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-29) - 4*a(n-30) + 6*a(n-31) - 4*a(n-32) + a(n-33) for n > 32.

%F G.f.: x^5*(-4*x^26 + 4*x^25 - 4*x^24 - x^23 + x^21 - 5*x^20 + 4*x^19 - 5*x^18 + x^17 - 3*x^15 + 2*x^14 - 4*x^13 + 2*x^12 - 3*x^11 + x^9 - 5*x^8 + 4*x^7 - 5*x^6 + x^5 - x^3 - 4*x^2 + 4*x - 4)/(x^33 - 4*x^32 + 6*x^31 - 4*x^30 + x^29 - x^4 + 4*x^3 - 6*x^2 + 4*x - 1). (End)

%t Table[Floor[Times@@(n-Range[0,3])/29],{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1},{0,0,0,0,0,4,12,28,57,104,173,273,409,591,828,1129,1506,1969,2532,3207,4009,4953,6053,7328,8793,10468,12372,14524,16944,19656,22680,26040,29760},50] (* _Harvey P. Dale_, Jun 09 2024 *)

%o (PARI) a(n)=n*(n-1)*(n-2)*(n-3)\29 \\ _Charles R Greathouse IV_, Oct 18 2022

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_.