A121496 Run lengths of successive numbers in A068225.

1, 2, 2, 1, 3, 4, 4, 3, 5, 6, 6, 5, 7, 8, 8, 7, 9, 10, 10, 9, 11, 12, 12, 11, 13, 14, 14, 13, 15, 16, 16, 15, 17, 18, 18, 17, 19, 20, 20, 19, 21, 22, 22, 21, 23, 24, 24, 23, 25, 26, 26, 25, 27, 28, 28, 27, 29, 30, 30, 29, 31, 32, 32, 31, 33, 34, 34, 33, 35, 36, 36, 35, 37, 38, 38

Offset

1,2

Comments

A000027 and A103889 are bisections.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

a(2*k-1) = k, a(4*k) = 2*k-1, a(4*k-2) = 2*k, for k >= 1.

From Colin Barker, Apr 08 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5.

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

a(n) = (2*n+1-4*cos(n*Pi/2)-cos(n*Pi))/4. - Wesley Ivan Hurt, Oct 02 2017

Example

The fifth run of successive numbers in A068225 is 8, 9, 10 with run length three so a(5) = 3.

Mathematica

Rest@ CoefficientList[Series[x (1 + x - x^3 + x^4)/((1 - x)^2*(1 + x) (1 + x^2)), {x, 0, 75}], x] (* Michael De Vlieger, Oct 02 2017 *)

Prog

(PARI) a(n) = if(n%2==1, (n+1)/2, if(n%4==0, (n/2)-1, (n/2)+1))
for(n=1, 80, print1(a(n), ", "))
(PARI) Vec(x*(1+x-x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)) + O(x^100)) \\ Colin Barker, Apr 08 2016

Crossrefs

Cf. A000027, A068225, A103889.

Sequence in context: A246425 A286468 A102563 * A276325 A286548 A256134

Adjacent sequences: A121493 A121494 A121495 * A121497 A121498 A121499

Keyword

nonn,easy

Author

Rick L. Shepherd, Aug 03 2006

Status

approved