A145730 Partial sums of A108019.

0, 4, 40, 332, 2672, 21396, 171192, 1369564, 10956544, 87652388, 701219144, 5609753196, 44878025616, 359024204980, 2872193639896, 22977549119228, 183820392953888, 1470563143631172, 11764505149049448, 94116041192395660

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Oct 17 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Crossrefs

Cf. A108019, A145729.

Programs

Mathematica

lst={};s=0;Do[s+=(s+=(s+=n+s));AppendTo[lst,s],{n,0,5!}];lst
Accumulate[NestList[8#+4&,0,20]] (* or *) LinearRecurrence[{10,-17,8},{0,4,40},20] (* Harvey P. Dale, Aug 08 2013 *)

PARI

concat(0, Vec(-4*x/((x-1)^2*(8*x-1)) + O(x^100))) \\ Colin Barker, Oct 28 2014

Formula

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

a(n) = 4*(8^(n+1)-7n-8)/49 = 4*A014831(n). - R. J. Mathar, Oct 21 2008

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

a(n) = A145729(n)/2. G.f.: -4*x / ((x-1)^2*(8*x-1)). - Colin Barker, Oct 28 2014

Extensions

Edited by R. J. Mathar, Oct 21 2008