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%I #14 Sep 26 2024 05:28:37
%S 6,27,73,155,285,476,742,1098,1560,2145,2871,3757,4823,6090,7580,9316,
%T 11322,13623,16245,19215,22561,26312,30498,35150,40300,45981,52227,
%U 59073,66555,74710,83576,93192,103598,114835,126945,139971,153957
%N Partial sums of A051941.
%C Inverse binomial transform gives 6, 21, 25, 11, 1, 0, 0, ... (0 continued). - _R. J. Mathar_, May 17 2008
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = Sum_{j=8..n} Sum_{k=8..j} ((k*(k+1)/2)-30). [corrected by _Jason Yuen_, Sep 26 2024]
%F a(n) = Sum_{j=8..n} (1/6)*(j-7)*(j^2+10*j-108).
%F a(n) = (n-6)(n-7)(n^2+19n-144)/24. O.g.f: x^8(6-3x-2x^2)/(1-x)^5. - _R. J. Mathar_, May 17 2008
%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) with a(8)=6, a(9)=27, a(10)=73, a(11)=155, a(12)=285. - _Harvey P. Dale_, Oct 20 2013
%t Accumulate[LinearRecurrence[{4,-6,4,-1},{6,21,46,82},50]] (* or *) LinearRecurrence[{5,-10,10,-5,1},{6,27,73,155,285},50] (* _Harvey P. Dale_, Oct 20 2013 *)
%Y Cf. A051941.
%K easy,nonn
%O 8,1
%A _Jonathan Vos Post_, May 10 2008
%E Corrected and extended by _R. J. Mathar_, May 17 2008