A276805 a(n) = numerator((n^2 + 3*n + 2)/n^3).

6, 3, 20, 15, 42, 7, 72, 45, 110, 33, 156, 91, 210, 30, 272, 153, 342, 95, 420, 231, 506, 69, 600, 325, 702, 189, 812, 435, 930, 124, 1056, 561, 1190, 315, 1332, 703, 1482, 195, 1640, 861, 1806, 473, 1980, 1035, 2162, 282, 2352, 1225, 2550, 663, 2756, 1431, 2970, 385

Offset: 1

Author

Pietro Tiaraju Giavarina dos Santos, Sep 17 2016

Keywords

• nonn
• easy
• frac

Examples

			a(1) = numerator((n^2 + 3*n + 2)/n^3)  = 1^2+3*1+2/1^3 = 6.
		

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).

Crossrefs

Cf. A277542.

Programs

Mathematica

Table[Numerator[(n^2 + 3*n + 2)/n^3], {n, 1, 100}]

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

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