A022411 a(n) = a(n-1) + a(n-2) + 1, with a(0)=3, a(1)=12.

3, 12, 16, 29, 46, 76, 123, 200, 324, 525, 850, 1376, 2227, 3604, 5832, 9437, 15270, 24708, 39979, 64688, 104668, 169357, 274026, 443384, 717411, 1160796, 1878208, 3039005, 4917214, 7956220, 12873435, 20829656, 33703092, 54532749, 88235842, 142768592, 231004435, 373773028, 604777464

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..4500

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

Formula

From R. J. Mathar, Mar 11 2011: (Start)

a(n+1) - a(n) = A022132(n-1).

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

Mathematica

LinearRecurrence[{2, 0, -1}, {3, 12, 16}, 40] (* Harvey P. Dale, Jan 26 2014 *)

Prog

(PARI) x='x+O('x^30); Vec((3+6*x-8*x^2)/((x-1)*(x^2+x-1))) \\ G. C. Greubel, Feb 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3+6*x-8*x^2)/((x-1)*(x^2+x-1)))); // G. C. Greubel, Feb 28 2018

Crossrefs

Sequence in context: A192786 A277738 A064106 * A115229 A224924 A136047

Adjacent sequences: A022408 A022409 A022410 * A022412 A022413 A022414

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(31) onward added by G. C. Greubel, Feb 28 2018

Status

approved