OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,1).
FORMULA
From Colin Barker, Sep 18 2016: (Start)
a(n) = 3*a(n-8)-3*a(n-16)+a(n-24) for n>24.
G.f.: x*(6 +3*x +20*x^2 +15*x^3 +42*x^4 +7*x^5 +72*x^6 +45*x^7 +92*x^8 +24*x^9 +96*x^10 +46*x^11 +84*x^12 +9*x^13 +56*x^14 +18*x^15 +30*x^16 +5*x^17 +12*x^18 +3*x^19 +2*x^20 +x^23) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3).
(End)
a(n) = a(n-8)*(n^2+3*n+2)/(n^2-13*n+42), for n>8. - Gionata Neri, Feb 25 2017
EXAMPLE
a(1) = numerator((n^2 + 3*n + 2)/n^3) = 1^2+3*1+2/1^3 = 6.
MATHEMATICA
Table[Numerator[(n^2 + 3*n + 2)/n^3], {n, 1, 100}]
PROG
(PARI) a(n) = numerator((n^2 + 3*n + 2)/n^3); \\ Michel Marcus, Sep 18 2016
(PARI) Vec(x*(6 +3*x +20*x^2 +15*x^3 +42*x^4 +7*x^5 +72*x^6 +45*x^7 +92*x^8 +24*x^9 +96*x^10 +46*x^11 +84*x^12 +9*x^13 +56*x^14 +18*x^15 +30*x^16 +5*x^17 +12*x^18 +3*x^19 +2*x^20 +x^23) / ((1 -x)^3*(1 +x)^3*(1 +x^2)^3*(1 +x^4)^3) + O(x^100)) \\ Colin Barker, Oct 20 2016
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
Pietro Tiaraju Giavarina dos Santos, Sep 17 2016
STATUS
approved