A152897 Partial sums of A152896.

0, 3, 18, 73, 256, 844, 2709, 8596, 27146, 85560, 269464, 848400, 2670859, 8407805, 26467163, 83316232, 262271397, 825604226, 2598919135, 8181135469, 25753388928, 81069068693, 255197243733, 803335158081, 2528817970143

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-18,23,-16,6,-1).

Crossrefs

Cf. A152891, A152895, A152896.

Programs

Mathematica

lst={};a=b=c=s=0;Do[c+=n+a;b+=n+c;a+=n+b;s+=a;AppendTo[lst,s],{n,0,2*4!}];lst
Rest[CoefficientList[Series[x^2(3-3x+x^2)/((1-x)^3(1-4x+3x^2-x^3)),{x,0,40}],x]]  (* Harvey P. Dale, Mar 11 2011 *)
LinearRecurrence[{7,-18,23,-16,6,-1},{0,3,18,73,256,844},30] (* Harvey P. Dale, Feb 07 2015 *)

Formula

a(n)=A124820(n)-A000217(n+1). G.f.: x^2(3-3x+x^2)/((1-x)^3*(1-4x+3x^2-x^3)). [From R. J. Mathar, Dec 15 2008]

a(1)=0, a(2)=3, a(3)=18, a(4)=73, a(5)=256, a(6)=844, a(n)=7*a(n-1)- 18*a(n-2)+ 23*a(n-3)-16*a(n-4)+6*a(n-5)-a (n-6). - Harvey P. Dale, Feb 07 2015