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

1,5

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).

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

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 *)

Crossrefs

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

Sequence in context: A127712 A305840 A178113 * A000014 A114851 A099364

Adjacent sequences: A032087 A032088 A032089 * A032091 A032092 A032093

Keyword

nonn,easy

Author

Christian G. Bower

Status

approved