A354789 a(2*n) = 9*2^n - 7, a(2*n+1) = 3*2^(n+2) - 7.

2, 5, 11, 17, 29, 41, 65, 89, 137, 185, 281, 377, 569, 761, 1145, 1529, 2297, 3065, 4601, 6137, 9209, 12281, 18425, 24569, 36857, 49145, 73721, 98297, 147449, 196601, 294905, 393209, 589817, 786425, 1179641, 1572857, 2359289, 3145721, 4718585, 6291449, 9437177, 12582905, 18874361, 25165817, 37748729, 50331641, 75497465

Offset: 0

Author

N. J. A. Sloane, Jul 14 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283.

Programs

Mathematica

LinearRecurrence[{1,2,-2},{2,5,11},100] (* Paolo Xausa, Oct 17 2023 *)
CoefficientList[Series[(2+3x+2x^2)/((1-x)(1-2x^2)),{x,0,50}],x] (* Harvey P. Dale, Jun 07 2024 *)

Formula

G.f.: (2 + 3*x + 2*x^2)/((1 - x)*(1 - 2*x^2)). - Stefano Spezia, Feb 05 2023

E.g.f.: - 7*cosh(x) + 9*cosh(sqrt(2)*x) - 7*sinh(x) + 6*sqrt(2)*sinh(sqrt(2)*x). - Stefano Spezia, Jul 25 2024