A241170 - OEIS

%I #29 Oct 11 2024 16:55:14

%S 6,25,67,145,275,476,770,1182,1740,2475,3421,4615,6097,7910,10100,

%T 12716,15810,19437,23655,28525,34111,40480,47702,55850,65000,75231,

%U 86625,99267,113245,128650,145576,164120,184382,206465,230475,256521,284715,315172

%N Steffensen's bracket function [n,n-3].

%H Vincenzo Librandi, <a href="/A241170/b241170.txt">Table of n, a(n) for n = 3..1000</a>

%H Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Sheila Sundaram, and Lei Xue, <a href="https://arxiv.org/abs/2407.08158">Topology of Cut Complexes II</a>, arXiv:2407.08158 [math.CO], 2024. See p. 15.

%H J. F. Steffensen, <a href="http://dx.doi.org/10.1080/03461238.1928.10416863">On a class of polynomials and their application to actuarial problems</a>, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F See A241168.

%F a(n) = (n-2)*(n-1)*(24 + 7*n + 3*n^2)/24. - _Vaclav Kotesovec_, Apr 23 2014

%F From _Vincenzo Librandi_, Dec 12 2014: (Start)

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

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.(End)

%p with(combinat);

%p T:=proc(n,k) add(stirling2(n,s+1)*s!/k!,s=k..n-1); end;

%p [seq(T(n,n-3),n=3..16)];

%t Table[(n-2)*(n-1)*(24 + 7*n + 3*n^2)/24,{n,3,20}] (* _Vaclav Kotesovec_, Apr 23 2014 *)

%t CoefficientList[Series[(6 - 5 x + 2 x^2) / (1 - x)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 12 2014 *)

%o (Magma) [(n-2)*(n-1)*(24+7*n+3*n^2)/24: n in [3..50]]; // _Vincenzo Librandi_, Dec 12 2014

%o (Magma) I:=[6,25,67,145,275]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Dec 12 2014

%o (PARI) for(n=3,30, print1((n-2)*(n-1)*(24+7*n+3*n^2)/24, ", ")) \\ _G. C. Greubel_, Feb 07 2018

%Y A diagonal of the triangular array in A241168.

%K nonn,easy

%O 3,1

%A _N. J. A. Sloane_, Apr 22 2014