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 A178242 Numerator of n*(5+n)/((n+1)*(n+4)). 8

%I

%S 0,3,7,6,9,25,33,21,26,63,75,44,51,117,133,75,84,187,207,114,125,273,

%T 297,161,174,375,403,216,231,493,525,279,296,627,663,350,369,777,817,

%U 429,450,943,987,516,539,1125,1173,611,636

%N Numerator of n*(5+n)/((n+1)*(n+4)).

%C The numerator of A176027(n)/A001793(n+1). The reduced fractions are 0, 3/5, 7/9, 6/7, 9/10, 25/27, 33/35, 21/22, 26/27, 63/65, 75/77, 44/45, ..

%C The sequence of differences denominator(n) - numerator(n) =1,2,2,1... =A014695(n). Denominator: A160050(n+2).

%H Vincenzo Librandi, <a href="/A178242/b178242.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-6,10,-12,12,-10,6,-3,1).

%F a(n) = A060819(n)*A060819(n+5).

%F a(n) = +3*a(n-1) -6*a(n-2) +10*a(n-3) -12*a(n-4) +12*a(n-5) -10*a(n-6) +6*a(n-7) -3*a(n-8) +a(n-9).

%F a(n) = 3*a(n-4) -3*a(n-8) +a(n-12).

%F G.f.: x*(-3+2*x-3*x^2-3*x^3+x^7) / ( (x-1)^3*(x^2+1)^3 ).

%F a(n) = n*(n+5)*((-1)^((2*n-(-1)^n-3)/4)+3)/8 = n*(n+5)*(3-i^(n*(n+1)))/8, where i=sqrt(-1); also a(n) = a(n-4)*A028557(n)/A028557(n-4) for n>4. - Bruno Berselli, Dec 30 2010

%p A178242 := proc(n) n*(5+n)/(n+1)/(n+4) ; numer(%) ;end proc:

%p seq(A178242(n),n=0..80) ; # R. J. Mathar, Dec 20 2010

%t f[n_] := n/GCD[n, 4]; Array[f[#] f[# + 5] &, 50, 0]

%o (MAGMA) [Floor(n*(n+5)*((-1)^((2*n-(-1)^n-3)/4)+3)/8) : n in [0..50]]; // Vincenzo Librandi, Oct 08 2011

%K nonn,easy,frac

%O 0,2

%A _Paul Curtz_, Dec 20 2010

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Last modified May 19 15:07 EDT 2013. Contains 225432 sequences.