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

1,2

Links

Table of n, a(n) for n=1..25.

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

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

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 *)

Crossrefs

Cf. A152891, A152895, A152896.

Sequence in context: A073961 A305623 A280804 * A059393 A301820 A094033

Adjacent sequences: A152894 A152895 A152896 * A152898 A152899 A152900

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

Status

approved