A238315 An oscillating sequence: a(n) = n^2 + 2^(n-1) - 2*a(n-1), n>0, with a(1) = 1.

1, 4, 5, 14, 13, 42, 29, 134, 69, 474, 197, 1798, 669, 7050, 2509, 28006, 9813, 111770, 38965, 446758, 155501, 1786634, 621565, 7146054, 2485733, 28583642, 9942309, 114333894, 39768509, 457334794, 159073197, 1829338278

Offset

1,2

Comments

For large n: a(2n)/a(2n-1) -> 23/2; a(2n+1)/a(2n) -> 8/23.

Related oscillating sequences can be formed by changing the offset of the exponent in the second term on the right-hand side of the definition (i.e., the power of 2) from (n-1) to n, (n+1), (n+2,) etc. In all such cases the values of a(2n-1) stays constant: 1, 5, 13, 29, 69, 197, 669, ... which is also given as A239367.

For large n, this and the related sequences all obey a(n)/a(n-2) -> 4, as the second term is dominant.

Links

Richard R. Forberg, Table of n, a(n) for n = 1..32

Index entries for linear recurrences with constant coefficients, signature (3,1,-11,12,-4).

Formula

G.f.: -x*(2*x^4-6*x^3+8*x^2-x-1) / ((x-1)^3*(2*x-1)*(2*x+1)). - Colin Barker, Mar 31 2014

Prog

(PARI) Vec(-x*(2*x^4-6*x^3+8*x^2-x-1)/((x-1)^3*(2*x-1)*(2*x+1)) + O(x^100)) \\ Colin Barker, Mar 31 2014

Crossrefs

Cf. A239367.

Sequence in context: A082312 A239615 A195747 * A091311 A008540 A290810

Adjacent sequences: A238312 A238313 A238314 * A238316 A238317 A238318

Keyword

nonn,easy

Author

Richard R. Forberg, Mar 30 2014

Status

approved