A258321 a(n) = Fibonacci(n) + n*Lucas(n).

0, 2, 7, 14, 31, 60, 116, 216, 397, 718, 1285, 2278, 4008, 7006, 12179, 21070, 36299, 62304, 106588, 181812, 309305, 524942, 888977, 1502474, 2534736, 4269050, 7178911, 12054926, 20215927, 33859908, 56646980, 94667088, 158045413, 263604046, 439272349

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = -a(-n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4).

a(n) = (n+1)*Fibonacci(n+1) + (n-1)*Fibonacci(n-1).

a(n) = 2*A001629(n+1) + 3*A001629(n) - 2*A001629(n-1) for n>0.

Sum_{i>0} 1/a(i) = .782177794921758720...

Mathematica

Table[Fibonacci[n] + n LucasL[n], {n, 0, 40}] (* or *) LinearRecurrence[{2, 1, -2, -1}, {0, 2, 7, 14}, 40]

Prog

(Sage) [fibonacci(n)+n*lucas_number2(n, 1, -1) for n in (0..40)]
(Magma) [Fibonacci(n)+n*Lucas(n): n in [0..40]]

Crossrefs

Cf. A061705: n*Fibonacci(n)+Lucas(n) = (n+1)*Fibonacci(n+1)-(n-1)*Fibonacci(n-1) with n>0.

Cf. A000032, A000045, A001629.

Sequence in context: A221320 A221235 A224916 * A034791 A140253 A018453

Adjacent sequences: A258318 A258319 A258320 * A258322 A258323 A258324

Keyword

nonn,easy

Author

Bruno Berselli, May 26 2015

Status

approved