A173234 Expansion of x*(1+3*x^2-2*x^3+2*x^4-x^5)/((1+x)*(x-1)^2*(x^2+1)^2).

0, 1, 1, 3, 1, 2, 3, 5, 2, 3, 5, 7, 3, 4, 7, 9, 4, 5, 9, 11, 5, 6, 11, 13, 6, 7, 13, 15, 7, 8, 15, 17, 8, 9, 17, 19, 9, 10, 19, 21, 10, 11, 21, 23, 11, 12, 23, 25, 12, 13, 25, 27, 13, 14, 27, 29, 14, 15, 29, 31, 15, 16, 31, 33, 16, 17, 33, 35, 17, 18, 35, 37, 18, 19, 37, 39, 19, 20, 39, 41, 20

Offset

0,4

Comments

The fractions A005563(n+1)/A000290(n+1) are 3, 8/4, 15/9, 24/16...,

in reduced form = 3, 2, 5/3, 3/2, 7/5... = a(2n+3)/a(2n+2).

The sequence shows the denominator-numerator pairs of the fractions.

Links

Table of n, a(n) for n=0..80.

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

Formula

G.f.: x*(1+3*x^2-2*x^3+2*x^4-x^5)/((1+x)*(x-1)^2*(x^2+1)^2).

a(n) = +a(n-1) -a(n-2) +a(n-3) +a(n-4) -a(n-5) +a(n-6) -a(n-7).

a(2n) = A026741(n). a(2n+1) = A026741(n+2).

Mathematica

CoefficientList[Series[x*(1 + 3*x^2 - 2*x^3 + 2*x^4 - x^5)/((1 + x)*(x - 1)^2*(x^2 + 1)^2), {x, 0, 100}], x] (* Wesley Ivan Hurt, May 03 2017 *)

Crossrefs

Cf. A000290, A005563, A026741.

Sequence in context: A336233 A325845 A260116 * A205017 A334473 A165520

Adjacent sequences: A173231 A173232 A173233 * A173235 A173236 A173237

Keyword

nonn,less

Author

Paul Curtz, Feb 13 2010

Extensions

Edited by R. J. Mathar, Feb 24 2010

Status

approved