A294178 a(2n) = 2*n + 1, a(2n+1) = 6*n + 3.

1, 3, 3, 9, 5, 15, 7, 21, 9, 27, 11, 33, 13, 39, 15, 45, 17, 51, 19, 57, 21, 63, 23, 69, 25, 75, 27, 81, 29, 87, 31, 93, 33, 99, 35, 105, 37, 111, 39, 117, 41, 123, 43, 129, 45, 135, 47, 141, 49, 147, 51, 153

Offset: 0

Author

Paul Curtz, Jun 28 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A029578, A289296.

Programs

Mathematica

LinearRecurrence[{0,2,0,-1},{1,3,3,9},100] (* Paolo Xausa, Nov 13 2023 *)

PARI

Vec((1 + 3*x)*(1 + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jun 29 2018

Formula

a(n) = 2*a(n-2) - a(n-4).

a(n) = A289296(n+1) - A289296(n).

G.f.: (1 + 3*x)*(1 + x^2) / ((1 - x)^2*(1 + x)^2). - Colin Barker, Jun 29 2018