A182202 Fibonacci-type sequence based on bitwise inclusive-or: a(0) = 0, a(1) = 1 and a(n) = a(n-1) + (a(n-1) or a(n-2)).

0, 1, 2, 5, 12, 25, 54, 117, 236, 489, 982, 2005, 4012, 8105, 16214, 32597, 65196, 130729, 261462, 523605, 1047212, 2095785, 4191574, 8385877, 16771756, 33548969, 67097942, 134206805, 268413612, 536849065, 1073698134, 2147439957, 4294879916, 8589847209

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (1,3,-1,0,-2,-4).

Formula

From Chai Wah Wu, Oct 12 2023: (Start)

a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-5) - 4*a(n-6) for n > 7.

G.f.: x*(8*x^6 + 2*x^3 + x + 1)/(4*x^6 + 2*x^5 + x^3 - 3*x^2 - x + 1). (End)

Example

a(2) = 1 + (1 or 0) = 2, a(3) = 2 + (2 or 1) = 5.

Mathematica

t = {0, 1}; Do[AppendTo[t, t[[-1]] + BitOr[t[[-1]], t[[-2]]]], {n, 2, 50}]; t (* T. D. Noe, Apr 18 2012 *)

Prog

(Python)
def A182202_gen(): # generator of terms
    a, b = 0, 1
    yield a
    while True:
        yield b
        a, b = b, b+(a|b)
A182202_list = list(islice(A182202_gen(), 30)) # Chai Wah Wu, Oct 12 2023

Crossrefs

Sequence in context: A262667 A122439 A063807 * A116715 A117177 A287141

Adjacent sequences: A182199 A182200 A182201 * A182203 A182204 A182205

Keyword

nonn,base

Author

Alex Ratushnyak, Apr 17 2012

Status

approved