A259751 - OEIS

%I #41 Sep 06 2022 14:28:00

%S 8,16,32,40,56,64,80,88,104,112,128,136,152,160,176,184,200,208,224,

%T 232,248,256,272,280,296,304,320,328,344,352,368,376,392,400,416,424,

%U 440,448,464,472,488,496,512,520,536,544,560,568,584,592,608,616,632

%N Numbers that are congruent to {8, 16} mod 24.

%C Original name: Numbers n such that n/A259748(n) = 4.

%H Danny Rorabaugh, <a href="/A259751/b259751.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) = 1/4.

%F a(n) = 8*A001651. - _Danny Rorabaugh_, Oct 22 2015

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

%F a(n) = 12*n-2*(-1)^n-6.

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

%F G.f.: 8*x*(1+x+x^2) / ((1-x)^2*(1+x)).

%F (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/72. - _Amiram Eldar_, Dec 31 2021

%F E.g.f.: 2*(4 + (6*x - 3)*exp(x) - exp(-x)). - _David Lovler_, Sep 05 2022

%t A[n_] := A[n] = Sum[a b, {a, 1,  n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]/# == 1/4 & ]

%o (PARI) Vec(8*x*(1+x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Colin Barker_, Aug 26 2016

%Y Cf. A000914, A001651.

%Y Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259749, A259750, A259752, A259754, A259755.

%K nonn,easy

%O 1,1

%A _José María Grau Ribas_, Jul 06 2015

%E Better name from _Danny Rorabaugh_, Oct 22 2015