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Partial sums of A108019.
1

%I #14 May 11 2023 14:35:10

%S 0,4,40,332,2672,21396,171192,1369564,10956544,87652388,701219144,

%T 5609753196,44878025616,359024204980,2872193639896,22977549119228,

%U 183820392953888,1470563143631172,11764505149049448,94116041192395660

%N Partial sums of A108019.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).

%F a(n) = Sum_{i=0..n} A108019(i).

%F a(n) = 4*(8^(n+1)-7n-8)/49 = 4*A014831(n). - _R. J. Mathar_, Oct 21 2008

%F a(0)=0, a(1)=4, a(2)=40, a(n)=10*a(n-1)-17*a(n-2)+8*a(n-3). - _Harvey P. Dale_, Aug 08 2013

%F a(n) = A145729(n)/2. G.f.: -4*x / ((x-1)^2*(8*x-1)). - _Colin Barker_, Oct 28 2014

%t lst={};s=0;Do[s+=(s+=(s+=n+s));AppendTo[lst,s],{n,0,5!}];lst

%t Accumulate[NestList[8#+4&,0,20]] (* or *) LinearRecurrence[{10,-17,8},{0,4,40},20] (* _Harvey P. Dale_, Aug 08 2013 *)

%o (PARI) concat(0, Vec(-4*x/((x-1)^2*(8*x-1)) + O(x^100))) \\ _Colin Barker_, Oct 28 2014

%Y Cf. A108019, A145729.

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Oct 17 2008

%E Edited by _R. J. Mathar_, Oct 21 2008