A259750 - OEIS

%I #39 Sep 06 2022 14:23:58

%S 14,22,38,46,62,70,86,94,110,118,134,142,158,166,182,190,206,214,230,

%T 238,254,262,278,286,302,310,326,334,350,358,374,382,398,406,422,430,

%U 446,454,470,478,494,502,518,526,542,550,566,574,590,598,614,622,638

%N Numbers that are congruent to {14, 22} mod 24.

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

%H Danny Rorabaugh, <a href="/A259750/b259750.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F A259748(a(n))/a(n) = 1/2.

%F a(n) = 2*A168489(n) - _Danny Rorabaugh_, Oct 22 2015

%F From _Colin Barker_, Aug 26 2016: (Start)

%F a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.

%F G.f.: 2*x*(7+4*x+x^2) / ((1-x)^2*(1+x)).

%F (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/24 - log(2+sqrt(3))/(4*sqrt(3)). - _Amiram Eldar_, Dec 31 2021

%F E.g.f.: 2*(1 + 6*x*exp(x) - exp(-x)). - _David Lovler_, Sep 06 2022

%t A[n_] := A[n] = Sum[a b, {a, 1,  n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]/# == 1/2 & ]

%o (PARI) vector(100, n, 2*(6*n-(-1)^n)) \\ _Altug Alkan_, Oct 23 2015

%o (PARI) Vec(2*x*(7+4*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Colin Barker_, Aug 26 2016

%Y Cf. A000914, A168489, A259748.

%K nonn,easy

%O 1,1

%A _José María Grau Ribas_, Jul 04 2015

%E Better name from _Danny Rorabaugh_, Oct 22 2015