A060161 a(n) = 2^n - 1 + 2*Fibonacci(n-1).

1, 5, 9, 19, 37, 73, 143, 281, 553, 1091, 2157, 4273, 8479, 16849, 33521, 66755, 133045, 265337, 529455, 1056937, 2110681, 4216195, 8424029, 16834529, 33647167, 67258913, 134460513, 268828291, 537506533, 1074770281, 2149147727, 4297659833, 8594291209

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 (4, -4, -1, 2).

Formula

From R. J. Mathar, Jul 07 2009: (Start)

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

G.f.: -x*(1+x-7*x^2+4*x^3)/((x-1)*(2*x-1)*(x^2+x-1)). (End)

Maple

with(combinat, fibonacci): seq(2^n - 1 + 2 * fibonacci(n - 1), n=1..10);

Mathematica

Table[2^n-1+2*Fibonacci[n-1], {n, 40}] (* or *) LinearRecurrence[{4, -4, -1, 2}, {1, 5, 9, 19}, 40] (* Harvey P. Dale, Jul 30 2017 *)

Prog

(PARI) { for (n=1, 200, write("b060161.txt", n, " ", 2^n - 1 + 2*fibonacci(n - 1)); ) } \\ Harry J. Smith, Jul 02 2009

Crossrefs

Cf. A060160, A000045, A000079.

Sequence in context: A061202 A235799 A295966 * A282730 A082674 A292773

Adjacent sequences: A060158 A060159 A060160 * A060162 A060163 A060164

Keyword

nonn

Author

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

Extensions

More terms from Asher Auel, Mar 16 2001

Status

approved