A140590 Exchange successive pairs of terms of A000051.

3, 2, 9, 5, 33, 17, 129, 65, 513, 257, 2049, 1025, 8193, 4097, 32769, 16385, 131073, 65537, 524289, 262145, 2097153, 1048577, 8388609, 4194305, 33554433, 16777217, 134217729, 67108865, 536870913, 268435457, 2147483649, 1073741825, 8589934593, 4294967297, 34359738369

Offset: 0

Author

Paul Curtz, Jul 06 2008

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4).

Crossrefs

Cf. A000051.

Programs

Mathematica

LinearRecurrence[{1,4,-4},{3,2,9},35] (* or *) CoefficientList[Series[(3 - x - 5*x^2)/((1 - x)*(1 - 2*x)*(1 + 2*x)),{x,0,34}],x] (* or *) a[n_]:= 2^(n + (-1)^n) + 1;Array[a,35,0] (* James C. McMahon, Jul 12 2025 *)

PARI

a(n)={(1<Andrew Howroyd, Jan 03 2020

PARI

Vec((3 - x - 5*x^2)/((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ Andrew Howroyd, Jan 03 2020

Formula

From Andrew Howroyd, Jan 03 2020: (Start)

a(n) = 2^(n + (-1)^n) + 1.

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

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

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jan 03 2020