A354788 a(2*k) = 3*2^k - 3, a(2*k+1) = 2^(k+2) - 3.

0, 1, 3, 5, 9, 13, 21, 29, 45, 61, 93, 125, 189, 253, 381, 509, 765, 1021, 1533, 2045, 3069, 4093, 6141, 8189, 12285, 16381, 24573, 32765, 49149, 65533, 98301, 131069, 196605, 262141, 393213, 524285, 786429, 1048573, 1572861, 2097149, 3145725, 4194301, 6291453, 8388605, 12582909, 16777213, 25165821, 33554429, 50331645

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

Formula

a(n) = A136252(n-1). - R. J. Mathar, Jul 14 2022

G.f.: x*(1 + 2*x)/((x - 1)*(2*x^2 - 1)). - R. J. Mathar, Jul 14 2022

E.g.f.: 3*(cosh(sqrt(2)*x) - cosh(x)) - 3*sinh(x) + 2*sqrt(2)*sinh(sqrt(2)*x). - Stefano Spezia, Feb 04 2023

Maple

f1:=proc(n) if (n mod 2) = 1 then 2^((n+3)/2)-3 else 3*2^(n/2)-3; fi; end;
[seq(f1(n), n=0..45)];

Mathematica

LinearRecurrence[{1, 2, -2}, {0, 1, 3}, 100] (* Paolo Xausa, Oct 17 2023 *)

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. - N. J. A. Sloane, Jul 14 2022

Sequence in context: A320596 A227565 A136252 * A187212 A141325 A248604

Adjacent sequences: A354785 A354786 A354787 * A354789 A354790 A354791

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 13 2022

Status

approved