A210678 a(n) = a(n-1)+a(n-2)+n+2, a(0)=a(1)=1.

1, 1, 6, 12, 24, 43, 75, 127, 212, 350, 574, 937, 1525, 2477, 4018, 6512, 10548, 17079, 27647, 44747, 72416, 117186, 189626, 306837, 496489, 803353, 1299870, 2103252, 3403152, 5506435, 8909619, 14416087, 23325740, 37741862, 61067638, 98809537, 159877213, 258686789, 418564042

Offset: 0

Author

Alex Ratushnyak, May 09 2012

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Crossrefs

Cf. A081659: a(n)=a(n-1)+a(n-2)+n-5, a(0)=a(1)=1 (except first 2 terms and sign).

Cf. A001924: a(n)=a(n-1)+a(n-2)+n-4, a(0)=a(1)=1 (except first 4 terms).

Cf. A000126: a(n)=a(n-1)+a(n-2)+n-2, a(0)=a(1)=1 (except first term).

Cf. A066982: a(n)=a(n-1)+a(n-2)+n-1, a(0)=a(1)=1.

Cf. A030119: a(n)=a(n-1)+a(n-2)+n, a(0)=a(1)=1.

Cf. A210677: a(n)=a(n-1)+a(n-2)+n+1, a(0)=a(1)=1.

Programs

Mathematica

LinearRecurrence[{3,-2,-1,1},{1,1,6,12},40] (* Harvey P. Dale, Dec 10 2014 *)
nxt[{n_,a_,b_}]:={n+1,b,a+b+n+3}; NestList[nxt,{1,1,1},40][[;;,2]] (* Harvey P. Dale, Mar 19 2023 *)

Formula

From Colin Barker, Jun 30 2012: (Start)

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4).

G.f.: (1 -2*x + 5*x^2 - 3*x^3)/((1 - x)^2*(1 - x - x^2)). (End)