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

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

C. G. Bower, Transforms (2)

Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-2,0,-1,1,1).

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

Prog

(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

Crossrefs

Sequence in context: A291896 A018155 A227375 * A352079 A105044 A026008

Adjacent sequences: A032086 A032087 A032088 * A032090 A032091 A032092

Keyword

nonn,easy

Author

Christian G. Bower

Status

approved