cp's OEIS Frontend

A024869 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = floor( n/2 ), s = natural numbers >= 2, t = natural numbers >= 3.

%I A024869 #16 Jan 29 2016 07:19:42
%S A024869 8,10,27,32,61,70,114,128,190,210,293,320,427,462,596,640,804,858,
%T A024869 1055,1120,1353,1430,1702,1792,2106,2210,2569,2688,3095,3230,3688,
%U A024869 3840,4352,4522,5091,5280,5909,6118,6810,7040,7798,8050,8877,9152,10051,10350,11324,11648
%N A024869 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = floor( n/2 ), s = natural numbers >= 2, t = natural numbers >= 3.
%H A024869 Vincenzo Librandi, <a href="/A024869/b024869.txt">Table of n, a(n) for n = 2..1000</a>
%H A024869 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1)
%F A024869 G.f.: x^2*(8+2*x-7*x^2-x^3+2*x^4) / ((1+x)^3*(x-1)^4). - _R. J. Mathar_, Sep 25 2013
%F A024869 a(n) = 8*A058187(n-2) +2*A058187(n-3) -7*A058187(n-4) -A058187(n-5) +2*A058187(n-6). - _R. J. Mathar_, Sep 25 2013
%F A024869 From _Colin Barker_, Jan 29 2016: (Start)
%F A024869 a(n) = (4*n^3+3*((-1)^n+13)*n^2+4*(6*(-1)^n+17)*n+42*((-1)^n-1))/48.
%F A024869 a(n) = (2*n^3+21*n^2+46*n)/24 for n even.
%F A024869 a(n) = (2*n^3+18*n^2+22*n-42)/24 for n odd.
%F A024869 (End)
%t A024869 CoefficientList[Series[(8 + 2 x - 7 x^2 - x^3 + 2 x^4)/((1 + x)^3 (x - 1)^4), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 25 2013 *)
%o A024869 (PARI) Vec(x^2*(8+2*x-7*x^2-x^3+2*x^4)/((1+x)^3*(x-1)^4) + O(x^100)) \\ _Colin Barker_, Jan 29 2016
%K A024869 nonn,easy
%O A024869 2,1
%A A024869 _Clark Kimberling_