A011932 - OEIS

%I #19 Nov 03 2024 09:33:48

%S 0,0,0,0,1,5,16,38,76,137,229,360,540,780,1092,1489,1985,2596,3338,

%T 4228,5285,6529,7980,9660,11592,13800,16309,19145,22336,25910,29896,

%U 34325,39229,44640,50592,57120,64260,72049,80525,89728,99698,110476,122105,134629,148092,162540,178020,194580,212269,231137

%N a(n) =  floor( n*(n-1)*(n-2)*(n-3)/22 ).

%H G. C. Greubel, <a href="/A011932/b011932.txt">Table of n, a(n) for n = 0..2500</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,0,0,0,0,0,0,1,-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-11) - 4*a(n-12) + 6*a(n-13) - 4*a(n-14) + a(n-15) for n > 14.

%F G.f.: x^4*(1 + x + 2*x^2 + x^4 + 2*x^5 + x^6 + 2*x^8 + x^9 + x^10)/((1-x)^4*(1-x^11)). (End)

%t Table[Floor[(n(n-1)(n-2)(n-3))/22],{n,0,60}] (* _Harvey P. Dale_, Nov 25 2017 *)

%o (PARI) a(n)=n*(n-1)*(n-2)*(n-3)\22 \\ _Charles R Greathouse IV_, Oct 18 2022

%o (Magma) [Floor(12*Binomial(n,4)/11): n in [0..80]]; // _G. C. Greubel_, Nov 03 2024

%o (SageMath) [12*binomial(n,4)//11 for n in range(81)] # _G. C. Greubel_, Nov 03 2024

%Y Cf. A011915.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Nov 03 2024