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

1, 1, 5, 10, 20, 36, 63, 107, 179, 296, 486, 794, 1293, 2101, 3409, 5526, 8952, 14496, 23467, 37983, 61471, 99476, 160970, 260470, 421465, 681961, 1103453, 1785442, 2888924, 4674396, 7563351, 12237779, 19801163, 32038976, 51840174, 83879186, 135719397, 219598621, 355318057

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

Programs

Mathematica

LinearRecurrence[{3, -2, -1, 1}, {1, 1, 5, 10}, 39] (* Jean-François Alcover, Oct 05 2017 *)

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 + 4*x^2 - 2*x^3)/((1 - x)^2*(1 - x - x^2)). (End)

E.g.f.: exp(x/2)*(25*cosh(sqrt(5)*x/2) + 7*sqrt(5)*sinh(sqrt(5)*x/2))/5 - exp(x)*(4 + x). - Stefano Spezia, Feb 24 2023