A187893 a(0)=1, a(1)=4, a(n) = a(n-1) + a(n-2) - 1.

1, 4, 4, 7, 10, 16, 25, 40, 64, 103, 166, 268, 433, 700, 1132, 1831, 2962, 4792, 7753, 12544, 20296, 32839, 53134, 85972, 139105, 225076, 364180, 589255, 953434, 1542688, 2496121, 4038808, 6534928, 10573735, 17108662, 27682396, 44791057, 72473452, 117264508

Offset

0,2

Links

Table of n, a(n) for n=0..38.

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

Formula

G.f.: -x*(-1-2*x+4*x^2) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Mar 15 2011

a(n) = 1+3*|A039834(n)| = 1+3*A000045(n). - R. J. Mathar, Mar 15 2011

Mathematica

Join[{a=1, b=4}, Table[c=a+b-1; a=b; b=c, {n, 100}]]
LinearRecurrence[{2, 0, -1}, {1, 4, 4}, 40] (* Harvey P. Dale, Jun 06 2020 *)

Prog

(PARI) a(n)=3*fibonacci(n)+1 \\ Charles R Greathouse IV, Oct 29 2016

Crossrefs

Cf. A000045, A000071, A001611, A001612, A039834, A187890.

Sequence in context: A238131 A212532 A109544 * A293678 A063984 A357270

Adjacent sequences: A187890 A187891 A187892 * A187894 A187895 A187896

Keyword

nonn,easy,changed

Author

Vladimir Joseph Stephan Orlovsky, Mar 15 2011

Status

approved