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

1,2

Links

Table of n, a(n) for n=1..27.

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

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

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 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 1, -6, 13, -13, 6]^(n-1)*[0; 2; 11; 40; 123])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A000217, A001906, A152891.

Sequence in context: A274326 A055329 A193005 * A308524 A335629 A000822

Adjacent sequences: A152892 A152893 A152894 * A152896 A152897 A152898

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2008

Status

approved