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A011939 a(n) = floor( n*(n-1)*(n-2)*(n-3)/29 ).

%I A011939 #20 Oct 27 2024 09:25:55
%S A011939 0,0,0,0,0,4,12,28,57,104,173,273,409,591,828,1129,1506,1969,2532,
%T A011939 3207,4009,4953,6053,7328,8793,10468,12372,14524,16944,19656,22680,
%U A011939 26040,29760,33864,38380,43332,48748,54657,61088,68069,75633,83809,92631,102132,112345,123306,135049,147612,161031,175345
%N A011939 a(n) = floor( n*(n-1)*(n-2)*(n-3)/29 ).
%H A011939 G. C. Greubel, <a href="/A011939/b011939.txt">Table of n, a(n) for n = 0..2500</a>
%H A011939 <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 A011939 From _Chai Wah Wu_, Aug 02 2020: (Start)
%F A011939 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 A011939 G.f.: x^5*(4 -4*x +4*x^2 +x^3 -x^5 +5*x^6 -4*x^7 +5*x^8 -x^9 +3*x^11 -2*x^12 +4*x^13 -2*x^14 +3*x^15 -x^17 +5*x^18 -4*x^19 +5*x^20 -x^21 +x^23 +4*x^24 -4*x^25 +4*x^26)/((1-x)^4*(1-x^29)). (End)
%t A011939 Table[Floor[Times@@(n-Range[0,3])/29],{n,0,60}] (* 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},60] (* _Harvey P. Dale_, Jun 09 2024 *)
%t A011939 Floor[24*Binomial[Range[0,60], 4]/29] (* _G. C. Greubel_, Oct 27 2024 *)
%o A011939 (PARI) a(n)=n*(n-1)*(n-2)*(n-3)\29 \\ _Charles R Greathouse IV_, Oct 18 2022
%o A011939 (Magma) [Floor(24*Binomial(n,4)/29): n in [0..60]]; // _G. C. Greubel_, Oct 27 2024
%o A011939 (SageMath) [24*binomial(n,4)//29 for n in range(61)] # _G. C. Greubel_, Oct 27 2024
%Y A011939 Cf. A011915.
%K A011939 nonn,easy
%O A011939 0,6
%A A011939 _N. J. A. Sloane_
%E A011939 More terms added by _G. C. Greubel_, Oct 27 2024