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Numbers that are congruent to {3,9,15,18,21} mod 24.
6

%I #30 Aug 30 2016 20:11:12

%S 3,9,15,18,21,27,33,39,42,45,51,57,63,66,69,75,81,87,90,93,99,105,111,

%T 114,117,123,129,135,138,141,147,153,159,162,165,171,177,183,186,189,

%U 195,201,207,210,213,219,225,231,234,237,243,249,255,258,261,267

%N Numbers that are congruent to {3,9,15,18,21} mod 24.

%C Original name: Numbers n such that n/A259748(n) = 3/2.

%H Danny Rorabaugh, <a href="/A259754/b259754.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F A259748(a(n))/a(n) = 2/3.

%F a(n) = 3*A047584(n). - _Michel Marcus_, Jul 18 2015

%F From _Colin Barker_, Aug 25 2016: (Start)

%F a(n) = a(n-1)+a(n-5)-a(n-6) for n>6.

%F G.f.: 3*x*(1+x)*(1+x+x^2+x^4) / ((1-x)^2*(1+x+x^2+x^3+x^4)).

%F (End)

%t A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}]; Select[Range[200], Mod[A[#], #]/# == 2/3 &]

%t Rest@ CoefficientList[Series[3 x (1 + x) (1 + x + x^2 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)), {x, 0, 56}], x] (* _Michael De Vlieger_, Aug 25 2016 *)

%t LinearRecurrence[{1,0,0,0,1,-1},{3,9,15,18,21,27},60] (* _Harvey P. Dale_, Aug 30 2016 *)

%o (PARI) Vec(3*x*(1+x)*(1+x+x^2+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4)) + O(x^100)) \\ _Colin Barker_, Aug 25 2016

%Y Cf. A000914.

%Y Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259749, A259750, A259751, A259752, A259755.

%K nonn,easy

%O 1,1

%A _José María Grau Ribas_, Jul 12 2015

%E Better name from _Danny Rorabaugh_, Oct 22 2015