A277542 - OEIS

%I #23 Oct 01 2017 00:17:02

%S 1,2,27,32,125,27,343,256,729,250,1331,864,2197,343,3375,2048,4913,

%T 1458,6859,4000,9261,1331,12167,6912,15625,4394,19683,10976,24389,

%U 3375,29791,16384,35937,9826,42875,23328,50653,6859,59319,32000,68921,18522,79507

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

%C Also, a(n) = denominator((n+2)/n^3). - _Danny Rorabaugh_, Sep 30 2017

%H Colin Barker, <a href="/A277542/b277542.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, 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).

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

%F 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).

%F a(n) = a(n-8)*n^3/(n-8)^3, for n > 8. - _Gionata Neri_, Feb 25 2017

%F 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

%t Table[Denominator[(n^2 + 3 n + 2)/n^3], {n, 43}] (* _Michael De Vlieger_, Feb 25 2017 *)

%o (PARI) a(n) = denominator((n^2 + 3*n + 2)/n^3) \\ _Colin Barker_, Oct 19 2016

%Y Cf. A276805.

%K nonn,frac,easy

%O 1,2

%A _Colin Barker_, Oct 19 2016