A377628 a(n) = a(n-1) + a(n-2) + 1 with a(0)=2 and a(1)=2.

2, 2, 5, 8, 14, 23, 38, 62, 101, 164, 266, 431, 698, 1130, 1829, 2960, 4790, 7751, 12542, 20294, 32837, 53132, 85970, 139103, 225074, 364178, 589253, 953432, 1542686, 2496119, 4038806, 6534926, 10573733, 17108660, 27682394, 44791055, 72473450, 117264506

Offset

0,1

Comments

a(n) = A000071(n+2) if the initial conditions are a(0)=0, a(1)=1, a(2)=2.

Links

Table of n, a(n) for n=0..37.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Formula

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

a(n) = 3*F(n+1)-1.

a(n) = F(n-1)+F(n+3)-1.

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

a(n) = A022086(n+1) - 1.

E.g.f.: 3*exp(x/2)*(5*cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2))/5 - exp(x). - Stefano Spezia, Nov 04 2024

Mathematica

LinearRecurrence[{2, 0, -1}, {2, 2, 5}, 38] (* James C. McMahon, Nov 21 2024 *)

Crossrefs

Cf. A000045, A000071, A022086.

Sequence in context: A335443 A042982 A340249 * A006367 A246807 A077902

Adjacent sequences: A377625 A377626 A377627 * A377629 A377630 A377631

Keyword

nonn,easy

Author

Enrique Navarrete, Nov 02 2024

Status

approved