A022409 a(n) = a(n-1) + a(n-2) + 1, with a(0)=3, a(1)=10.

3, 10, 14, 25, 40, 66, 107, 174, 282, 457, 740, 1198, 1939, 3138, 5078, 8217, 13296, 21514, 34811, 56326, 91138, 147465, 238604, 386070, 624675, 1010746, 1635422, 2646169, 4281592, 6927762, 11209355, 18137118, 29346474, 47483593, 76830068, 124313662, 201143731, 325457394, 526601126

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: ( 3+4*x-6*x^2 )/((x-1)*(x^2+x-1)). - R. J. Mathar, Mar 11 2011

a(n) = 3*Lucas(n+1) + Fibonacci(n+2) - 1. - Greg Dresden, Oct 10 2020

Mathematica

LinearRecurrence[{2, 0, -1}, {3, 10, 14}, 40] (* Harvey P. Dale, Dec 01 2015 *)
CoefficientList[Series[(3+4*x-6*x^2)/((x-1)*(x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, Mar 01 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(( 3+4*x-6*x^2 )/((x-1)*(x^2+x-1))) \\ G. C. Greubel, Mar 01 2018
(Magma) I:=[3, 10, 14]; [n le 3 select I[n] else 2*Self(n-1) - Self(n-3): n in [1..30]]; // G. C. Greubel, Mar 01 2018

Crossrefs

Sequence in context: A287115 A063796 A063221 * A245524 A023866 A024593

Adjacent sequences: A022406 A022407 A022408 * A022410 A022411 A022412

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(31) onward added by G. C. Greubel, Mar 01 2018

Status

approved