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%I A259749 #39 Jan 15 2022 15:04:53
%S A259749 1,2,5,7,10,11,13,17,19,23,25,26,29,31,34,35,37,41,43,47,49,50,53,55,
%T A259749 58,59,61,65,67,71,73,74,77,79,82,83,85,89,91,95,97,98,101,103,106,
%U A259749 107,109,113,115,119,121,122,125,127,130,131,133,137,139,143,145
%N A259749 Numbers that are congruent to {1,2,5,7,10,11,13,17,19,23} mod 24.
%C A259749 Original name: Numbers n such that A259748(n) = 0.
%H A259749 Danny Rorabaugh, Table of n, a(n) for n = 1..10000
%H A259749 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-2,2,-2,2,-1).
%F A259749 A259748(a(n)) = Sum_{x*y: x,y in Z/a(n)Z, x<>y} = 0.
%F A259749 G.f.: x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7) / ((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - _Colin Barker_, Aug 25 2016
%t A259749 A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #] == 0 & ]
%t A259749 Rest@ CoefficientList[Series[x (1 + x^2) (1 + 2 x^2 - x^3 + 2 x^4 - 2 x^5 + 3 x^6 + x^7)/((1 - x)^2*(1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)), {x, 0, 61}], x] (* _Michael De Vlieger_, Aug 25 2016 *)
%t A259749 Select[Range[150],MemberQ[{1,2,5,7,10,11,13,17,19,23},Mod[#,24]]&] (* or *) LinearRecurrence[{2,-2,2,-2,2,-2,2,-2,2,-1},{1,2,5,7,10,11,13,17,19,23},70] (* _Harvey P. Dale_, Jan 15 2022 *)
%o A259749 (PARI) Vec(x*(1+x^2)*(1+2*x^2-x^3+2*x^4-2*x^5+3*x^6+x^7)/((1-x)^2*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100)) \\ _Colin Barker_, Aug 25 2016
%Y A259749 Cf. A000914.
%Y A259749 Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259750, A259751, A259752, A259754, A259755.
%K A259749 nonn,easy
%O A259749 1,2
%A A259749 _José María Grau Ribas_, Jul 04 2015
%E A259749 Better name from _Danny Rorabaugh_, Oct 22 2015
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