A032090 "BHK" (reversible, identity, unlabeled) transform of 0,1,1,1...

0, 1, 1, 1, 2, 2, 4, 5, 10, 14, 26, 39, 69, 107, 183, 289, 484, 772, 1276, 2047, 3356, 5402, 8812, 14213, 23113, 37325, 60581, 97905, 158718, 256622, 415716, 672337, 1088662, 1760998, 2850646, 4611643, 7463885, 12075527

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• C. G. Bower, Transforms (2)
• Index entries for linear recurrences with constant coefficients, signature (2,1,-3,1,-1,0,1).

Crossrefs

For n>2, a(n) = A032089(n-1) + [n even], a(2n) = A032097(n-1).

Programs

Mathematica

CoefficientList[Series[- x (x^6 + x^5 - x^4 + 2 x^3 - 2 x^2 - x + 1)/((x - 1) (x^2 + x - 1) (x^4 + x^2 - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)
LinearRecurrence[{2,1,-3,1,-1,0,1},{0,1,1,1,2,2,4,5},40] (* Harvey P. Dale, Mar 31 2019 *)

Formula

G.f.: -x^2*(x^6+x^5-x^4+2*x^3-2*x^2-x+1) / ((x-1)*(x^2+x-1)*(x^4+x^2-1)). [Colin Barker, Dec 07 2012]

2*a(n) = 2+A000045(n-1) - |A051792(n+5)|, n>1. - R. J. Mathar, Mar 24 2023