login
a(n) = floor(n*(n-1)*(n-2)*(n-3)/31).
2

%I #25 Oct 27 2024 03:13:19

%S 0,0,0,0,0,3,11,27,54,97,162,255,383,553,774,1056,1409,1842,2369,3000,

%T 3750,4633,5663,6855,8226,9793,11574,13587,15851,18387,21216,24360,

%U 27840,31680,35904,40536,45603,51131,57147,63678,70753,78402,86655,95543

%N a(n) = floor(n*(n-1)*(n-2)*(n-3)/31).

%H Robert Israel, <a href="/A011941/b011941.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1).

%F G.f.: (3-x+x^2+2*x^4+x^5+x^7+2*x^9+x^10-x^12+5*x^13-4*x^14+5*x^15-x^16+x^18 +2*x^19+x^21+x^23+2*x^24+x^26-x^27+3*x^28)*x^5/((1-x)^4*(1-x^31)). - _Robert Israel_, Feb 12 2017

%p f:= n -> floor(n*(n-1)*(n-2)*(n-3)/31):

%p map(f, [$0..100]); # _Robert Israel_, Feb 12 2017

%t Floor[24*Binomial[Range[0, 60], 4]/31] (* _G. C. Greubel_, Oct 26 2024 *)

%o (PARI) a(n) = n*(n-1)*(n-2)*(n-3)\31; \\ _Altug Alkan_, Feb 12 2017

%o (Magma) [Floor(24*Binomial(n,4)/31): n in [0..60]]; // _G. C. Greubel_, Oct 26 2024

%o (SageMath) [24*binomial(n,4)//31 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_