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a(n) = floor( n*(n-1)*(n-2)*(n-3)/32 ).
2

%I #17 Oct 27 2024 09:26:08

%S 0,0,0,0,0,3,11,26,52,94,157,247,371,536,750,1023,1365,1785,2295,2907,

%T 3633,4488,5486,6641,7969,9487,11212,13162,15356,17813,20553,23598,

%U 26970,30690,34782,39270,44178,49533,55361,61688,68542,75952,83947,92557,101813,111746,122388,133773,145935,158907,172725

%N a(n) = floor( n*(n-1)*(n-2)*(n-3)/32 ).

%H G. C. Greubel, <a href="/A011942/b011942.txt">Table of n, a(n) for n = 0..2500</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1).

%F From _R. J. Mathar_, Apr 15 2010]: (Start)

%F a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -6*a(n-4) +6*a(n-5) -10*a(n-6) +10*a(n-7) -6*a(n-8) +6*a(n-9) -10*a(n-10) +10*a(n-11) -6*a(n-12) +6*a(n-13) -10*a(n-14) +10*a(n-15) -5*a(n-16) +a(n-17).

%F G.f.: x^5*(1-x+x^2)*(3-x-3*x^2+5*x^4-3*x^6-x^7+3*x^8)/((1-x)^5*(1+x^4)*(1+x^8) ). (End)

%t Floor[3*Binomial[Range[0,60], 4]/4] (* _G. C. Greubel_, Oct 26 2024 *)

%o (Magma) [Floor(3*Binomial(n,4)/4): n in [0..60]]; // _G. C. Greubel_, Oct 26 2024

%o (SageMath) [3*binomial(n,4)//4 for n in range(61)] # _G. C. Greubel_, Oct 26 2024

%Y Cf. A011915.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Oct 26 2024