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 A024854 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (natural numbers >= 3). 5

%I

%S 4,5,16,19,40,46,80,90,140,155,224,245,336,364,480,516,660,705,880,

%T 935,1144,1210,1456,1534,1820,1911,2240,2345,2720,2840,3264,3400,3876,

%U 4029,4560,4731,5320,5510,6160,6370,7084,7315,8096,8349,9200,9476,10400,10700,11700

%N a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (natural numbers >= 3).

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).

%F a(n) = sum_{i=1..floor(n/2)} i*(n-i+3) = -floor(n/2)*(floor(n/2)+1)*(2*floor(n/2)-3n-8)/6. - _Wesley Ivan Hurt_, Sep 20 2013

%F G.f. -x^2*(-4-x+x^2) / ( (1+x)^3*(x-1)^4 ). - _R. J. Mathar_, Sep 25 2013

%F a(n) = 4*A058187(n-2)+A058187(n-3)-A058187(n-4). - _R. J. Mathar_, Sep 25 2013

%F a(n) = (4*n^3+21*n^2+14*n-9+3*(n^2+6*n+3)*(-1)^n)/48. - _Luce ETIENNE_, Nov 14 2014

%p seq(sum(i*(k-i+3), i=1..floor(k/2)), k=2..70); # _Wesley Ivan Hurt_, Sep 20 2013

%t Table[-Floor[n/2] * (Floor[n/2] + 1) * (2 * Floor[n/2] - 3n - 8)/6, {n, 2, 100}] (* _Wesley Ivan Hurt_, Sep 20 2013 *)

%t CoefficientList[Series[- (- 4 - x + x^2)/((1 + x)^3 (x - 1)^4), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 31 2014 *)

%o (MAGMA) [(4*n^3+21*n^2+14*n-9+3*(n^2+6*n+3)*(-1)^n)/48: n in [2..60]]; // _Vincenzo Librandi_, Oct 31 2014

%Y Cf. A023855, A023856, A023857, A024305.

%K nonn,easy

%O 2,1

%A _Clark Kimberling_

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Last modified January 16 19:43 EST 2019. Contains 319206 sequences. (Running on oeis4.)