A069229 a(n) = n*(2^n + 1).

0, 3, 10, 27, 68, 165, 390, 903, 2056, 4617, 10250, 22539, 49164, 106509, 229390, 491535, 1048592, 2228241, 4718610, 9961491, 20971540, 44040213, 92274710, 192938007, 402653208, 838860825, 1744830490, 3623878683, 7516192796

Offset: 0

Author

Vladeta Jovovic, Apr 12 2002

Keywords

• nonn
• easy

Comments

Odd terms are multiples of 3. - Dario Piazzalunga, Jan 10 2013

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -13, 12, -4).

Crossrefs

Cf. A066524.

Programs

Mathematica

Table[n*2^n+n,{n,0,3*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2010 *)
LinearRecurrence[{6,-13,12,-4},{0,3,10,27},30] (* Harvey P. Dale, May 06 2021 *)

Formula

Recurrence: a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).

G.f.: x*(3 - 8*x + 6*x^2)/(1-x)^2/(1 - 2*x)^2.

a(n) = n+A036289(n). - R. J. Mathar, Jun 17 2020