A083322 a(n) = 2^n - A081374(n).

1, 2, 6, 11, 22, 42, 85, 170, 342, 683, 1366, 2730, 5461, 10922, 21846, 43691, 87382, 174762, 349525, 699050, 1398102, 2796203, 5592406, 11184810, 22369621, 44739242, 89478486, 178956971, 357913942, 715827882, 1431655765, 2863311530, 5726623062

Offset: 1

Author

David Applegate, Aug 22 2003

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A081374.

Trisections: A082365, A007613, A132804.

Programs

Magma

I:=[1,2,6,11]; [n le 4 select I[n] else 2*Self(n-1)-Self(n-3)+2*Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jul 08 2016

Mathematica

CoefficientList[Series[(1 + 2 x^2) / ((1 - 2 x) (1 + x) (1 - x + x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 08 2016 *)
LinearRecurrence[{2,0,-1,2},{1,2,6,11},40] (* Harvey P. Dale, Jan 30 2024 *)

Formula

G.f.: x*(1+2*x^2) / ( (1-2*x)*(1+x)*(1-x+x^2) ). - R. J. Mathar, May 27 2011

From Paul Curtz, May 27 2011: (Start)

a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4).

a(n)+a(n+3) = 3*2^(n+1) = A007283(n+1).

a(n+6)-a(n) = 21*2^(n+1) = A175805(n+1).

(End)