A145655 Partial sums of A080674.

4, 24, 108, 448, 1812, 7272, 29116, 116496, 466020, 1864120, 7456524, 29826144, 119304628, 477218568, 1908874332, 7635497392, 30541989636, 122167958616, 488671834540, 1954687338240, 7818749353044, 31274997412264

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Oct 16 2008

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -9, 4).

Crossrefs

Cf. A080674.

Programs

Mathematica

lst={};s=0;Do[s+=(s+=(s+=n));AppendTo[lst,s],{n,3*4!}];lst
Accumulate[Table[4(4^n-1)/3,{n,0,40}]] (* or *) LinearRecurrence[{6,-9,4},{0,4,24},40] (* Harvey P. Dale, Nov 27 2013 *)

Formula

a(n) = sum_{i=0..n} A080674(i). a(n+1)-a(n) = A080674(n+1).

a(n) = 4*(4^(n+1)-3n-4)/9 = 4*A014825(n). - R. J. Mathar, Oct 21 2008

G.f.: 4x/((1-x)^2(1-4x)). - R. J. Mathar, Oct 21 2008

a(1)=4, a(2)=24, a(3)=108, a(n)=6*a(n-1)-9*a(n-2)+4*a(n-3). - Harvey P. Dale, Nov 27 2013

Extensions

Edited by R. J. Mathar, Oct 21 2008