A152895 Partial sums of A152891.

0, 2, 11, 40, 123, 349, 951, 2539, 6710, 17645, 46290, 121302, 317706, 831920, 2178173, 5702734, 14930181, 39087979, 102333945, 267914065, 701408480, 1836311627, 4807526676, 12586268700, 32951279748, 86267570894, 225851433311

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1).

Crossrefs

Cf. A000217, A001906, A152891.

Programs

Mathematica

lst={};a=b=s=0;Do[b+=n+a;a+=n+b;s+=a;AppendTo[lst,s],{n,0,2*4!}];lst
Accumulate[LinearRecurrence[{5,-8,5,-1},{0,2,9,29},30]] (* or *) LinearRecurrence[{6,-13,13,-6,1},{0,2,11,40,123},30] (* Harvey P. Dale, Mar 26 2015 *)

Formula

From R. J. Mathar, Jan 08 2009: (Start)

G.f.: x^2*(2-x)/((1-3x+x^2)*(1-x)^3).

a(n) = A001906(n+1)-A000217(n+1). (End)

a(1)=0, a(2)=2, a(3)=11, a(4)=40, a(5)=123, a(n)=6*a(n-1)-13*a(n-2)+ 13*a(n-3)- 6*a(n-4)+a(n-5). - Harvey P. Dale, Mar 26 2015