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

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

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

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)

Prog

(PARI) a(n)={(1<<bitxor(n, 1)) + 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

Crossrefs

Cf. A000051.

Sequence in context: A319107 A228323 A350831 * A329211 A164279 A289053

Adjacent sequences: A140587 A140588 A140589 * A140591 A140592 A140593

Keyword

nonn,easy

Author

Paul Curtz, Jul 06 2008

Extensions

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

Status

approved