A032089 "BHK" (reversible, identity, unlabeled) transform of 1,0,1,0...(odds).

1, 0, 1, 1, 2, 3, 5, 9, 14, 25, 39, 68, 107, 182, 289, 483, 772, 1275, 2047, 3355, 5402, 8811, 14213, 23112, 37325, 60580, 97905, 158717, 256622, 415715, 672337, 1088661, 1760998, 2850645, 4611643, 7463884, 12075527, 19541994, 31617521, 51163695, 82781216, 133951675

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• easy

Links

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

Programs

Mathematica

LinearRecurrence[{1,3,-2,-2,0,-1,1,1},{1,0,1,1,2,3,5,9},42] (* Stefano Spezia, Apr 01 2025 *)

PARI

Vec((1-x-2*x^2+2*x^3+x^6)/((1-x)*(1+x)*(1-x-x^2)*(1-x^2-x^4)) + O(x^40)) \\ Andrew Howroyd, Aug 31 2018

Formula

G.f.: x*(1-x-2*x^2+2*x^3+x^6)/((1-x)*(1+x)*(1-x-x^2)*(1-x^2-x^4)).

a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) + a(n-8) for n > 8. - Andrew Howroyd, Aug 31 2018

2*a(n) = 2*A000035(n) + A000045(n) - A053602(n). - R. J. Mathar, Mar 02 2022