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A024875 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor( n/2 ), s = natural numbers >= 3.

%I A024875 #20 Jan 29 2016 08:18:53
%S A024875 12,15,38,45,82,94,148,166,240,265,362,395,518,560,712,764,948,1011,
%T A024875 1230,1305,1562,1650,1948,2050,2392,2509,2898,3031,3470,3620,4112,
%U A024875 4280,4828,5015,5622,5829,6498,6726,7460,7710,8512,8785,9658,9955,10902,11224,12248,12596
%N A024875 a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = floor( n/2 ), s = natural numbers >= 3.
%H A024875 Vincenzo Librandi, <a href="/A024875/b024875.txt">Table of n, a(n) for n = 2..1000</a>
%H A024875 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1)
%F A024875 G.f.: x^2*(12+3*x-13*x^2-2*x^3+4*x^4) / ((1+x)^3*(x-1)^4). - _R. J. Mathar_, Sep 25 2013
%F A024875 a(n) = 12*A058187(n-2) +3*A058187(n-3) -13*A058187(n-4) -2*A058187(n-5) +4*A058187(n-6). - _R. J. Mathar_, Sep 25 2013
%F A024875 From _Colin Barker_, Jan 29 2016: (Start)
%F A024875 a(n) = (4*n^3+3*((-1)^n+19)*n^2+2*(15*(-1)^n+61)*n+75*((-1)^n-1))/48.
%F A024875 a(n) = (2*n^3+30*n^2+76*n)/24 for n even.
%F A024875 a(n) = (2*n^3+27*n^2+46*n-75)/24 for n odd. (End)
%t A024875 CoefficientList[Series[(12 + 3 x - 13 x^2 - 2 x^3 + 4 x^4)/((1 + x)^3 (x - 1)^4), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 25 2013 *)
%t A024875 LinearRecurrence[{1,3,-3,-3,3,1,-1},{12,15,38,45,82,94,148},50] (* _Harvey P. Dale_, Jul 21 2015 *)
%o A024875 (PARI) Vec(x^2*(12+3*x-13*x^2-2*x^3+4*x^4)/((1+x)^3*(x-1)^4) + O(x^100)) \\ _Colin Barker_, Jan 29 2016
%K A024875 nonn,easy
%O A024875 2,1
%A A024875 _Clark Kimberling_