A051032 Summatory Rudin-Shapiro sequence for 2^(n-1).

2, 3, 3, 5, 5, 9, 9, 17, 17, 33, 33, 65, 65, 129, 129, 257, 257, 513, 513, 1025, 1025, 2049, 2049, 4097, 4097, 8193, 8193, 16385, 16385, 32769, 32769, 65537, 65537, 131073, 131073, 262145, 262145, 524289, 524289, 1048577, 1048577, 2097153

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Rudin-Shapiro Sequence.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

Crossrefs

Cf. A014081, A020985, A020986, A000051.

Programs

Mathematica

d2n[n_]:=Module[{x=2^n+1},{x,x}];Join[{2},Flatten[Array[d2n,30]]] (* Harvey P. Dale, May 26 2011 *)

Formula

Apart from leading term, just A000051 (2^n + 1) doubled up.

G.f.: -x*(-2 - x + 4*x^2)/((x - 1)*(2*x^2 - 1)). - R. J. Mathar, Jul 15 2016

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3). - Wesley Ivan Hurt, Aug 19 2022

E.g.f.: cosh(x) + cosh(sqrt(2)*x) + sinh(x) + sinh(sqrt(2)*x)/sqrt(2) - 2. - Stefano Spezia, Feb 05 2023