A060160 a(n) = 2^n - 1 + Fibonacci(n-1)*2^(n+1).

1, 11, 23, 79, 223, 703, 2175, 6911, 22015, 70655, 227327, 733183, 2367487, 7651327, 24739839, 80019455, 258867199, 837550079, 2710044671, 8769241087, 28376563711, 91825897471, 297149661183, 961586135039, 3111737360383, 10069752152063

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (5, -4, -8, 8).

Formula

From R. J. Mathar, Feb 06 2010: (Start)

a(n) = 5*a(n-1) - 4*a(n-2) - 8*a(n-3) + 8*a(n-4).

G.f.: x*(1+6*x-28*x^2+16*x^3)/ ((1-x) * (2*x-1) * (4*x^2+2*x-1)). (End)

Maple

with(combinat, fibonacci): seq(2^n - 1 + fibonacci(n - 1)*2^(n+1), n=1..25);

Mathematica

Table[2^n-1+Fibonacci[n-1]2^(n+1), {n, 30}] (* or *) LinearRecurrence[{5, -4, -8, 8}, {1, 11, 23, 79}, 30] (* Harvey P. Dale, Dec 19 2021 *)

Prog

(PARI) a(n) = { 2^n - 1 + fibonacci(n - 1)*2^(n + 1) } \\ Harry J. Smith, Jul 02 2009

Crossrefs

Cf. A060161, A000045 (Fibonacci).

Sequence in context: A195463 A104066 A184394 * A241973 A158021 A239638

Adjacent sequences: A060157 A060158 A060159 * A060161 A060162 A060163

Keyword

nonn,changed

Author

Pieter Gosselink (pieter_gosselink(AT)lotus.com), Mar 12 2001

Extensions

More terms from Asher Auel, Mar 16 2001

Status

approved