A277542 a(n) = denominator((n^2 + 3*n + 2)/n^3).

1, 2, 27, 32, 125, 27, 343, 256, 729, 250, 1331, 864, 2197, 343, 3375, 2048, 4913, 1458, 6859, 4000, 9261, 1331, 12167, 6912, 15625, 4394, 19683, 10976, 24389, 3375, 29791, 16384, 35937, 9826, 42875, 23328, 50653, 6859, 59319, 32000, 68921, 18522, 79507

Offset: 1

Author

Colin Barker, Oct 19 2016

Keywords

• nonn
• frac
• easy

Comments

Also, a(n) = denominator((n+2)/n^3). - Danny Rorabaugh, Sep 30 2017

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A276805.

Programs

Mathematica

Table[Denominator[(n^2 + 3 n + 2)/n^3], {n, 43}] (* Michael De Vlieger, Feb 25 2017 *)

PARI

a(n) = denominator((n^2 + 3*n + 2)/n^3) \\ Colin Barker, Oct 19 2016

Formula

a(n) = 4*a(n-8) - 6*a(n-16) + 4*a(n-24) - a(n-32) for n > 32.

G.f.: x*(1 + 2*x + 27*x^2 + 32*x^3 + 125*x^4 + 27*x^5 + 343*x^6 + 256*x^7 + 725*x^8 + 242*x^9 + 1223*x^10 + 736*x^11 + 1697*x^12 + 235*x^13 + 2003*x^14 + 1024*x^15 + 2003*x^16 + 470*x^17 + 1697*x^18 + 736*x^19 + 1223*x^20 + 121*x^21 + 725*x^22 + 256*x^23 + 343*x^24 + 54*x^25 + 125*x^26 + 32*x^27 + 27*x^28 + x^29 + x^30) / ((1 - x)^4*(1 + x)^4*(1 + x^2)^4*(1 + x^4)^4).

a(n) = a(n-8)*n^3/(n-8)^3, for n > 8. - Gionata Neri, Feb 25 2017

a(n) = n^3 / 2^min(v2(n+2),3*v2(n)), where v2(n) = A007814(n) is the 2-adic valuation of n. - Danny Rorabaugh, Sep 30 2017