A120727 a(n) = a(n-1) + a(n-2), starting with 110, 211.

110, 211, 321, 532, 853, 1385, 2238, 3623, 5861, 9484, 15345, 24829, 40174, 65003, 105177, 170180, 275357, 445537, 720894, 1166431, 1887325, 3053756, 4941081, 7994837, 12935918, 20930755, 33866673, 54797428, 88664101, 143461529

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..286

Tanya Khovanova, Recursive Sequences

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

Formula

a(0)=101, a(1)=110, a(n) = a(n-1) + a(n-2).

G.f.: (110*x + 101*x^2)/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

Mathematica

d = 10 M = {{0, 1, 0}, {0, 0, 1}, {1, d, d^2}} v[n_] := Table[Fibonacci[n + i], {i, 0, 2}] w[n_] := M.v[n] Table[w[n][[3]], {n, 0, 50}]
Transpose[NestList[Flatten[{Last[#], Total[#]}]&, {110, 211}, 40]][[1]] (* or *) Rest[CoefficientList[Series[(110x+101x^2)/(1-x-x^2), {x, 0, 41}], x]]  (* Harvey P. Dale, Mar 27 2011 *)
LinearRecurrence[{1, 1}, {110, 211}, 30] (* Harvey P. Dale, Jan 01 2023 *)

Prog

(Magma) [n le 2 select 101*n+9 else Self(n-1)+Self(n-2): n in [1..30]] // Bruno Berselli, Mar 28 2011
(PARI) a=vector(99); a[1]=110; a[2]=211; for(i=3, #a, a[i]=a[i-1]+a[i-2]); a \\ Charles R Greathouse IV, Jun 05 2011

Crossrefs

Cf. A000045.

Sequence in context: A249838 A103652 A032614 * A251230 A264447 A134213

Adjacent sequences: A120724 A120725 A120726 * A120728 A120729 A120730

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 19 2006

Extensions

Edited by N. J. A. Sloane, Dec 04 2006

Status

approved