# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a259751 Showing 1-1 of 1 %I A259751 #41 Sep 06 2022 14:28:00 %S A259751 8,16,32,40,56,64,80,88,104,112,128,136,152,160,176,184,200,208,224, %T A259751 232,248,256,272,280,296,304,320,328,344,352,368,376,392,400,416,424, %U A259751 440,448,464,472,488,496,512,520,536,544,560,568,584,592,608,616,632 %N A259751 Numbers that are congruent to {8, 16} mod 24. %C A259751 Original name: Numbers n such that n/A259748(n) = 4. %H A259751 Danny Rorabaugh, Table of n, a(n) for n = 1..10000 %H A259751 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). %F A259751 A259748(a(n))/a(n) = 1/4. %F A259751 a(n) = 8*A001651. - _Danny Rorabaugh_, Oct 22 2015 %F A259751 From _Colin Barker_, Aug 26 2016: (Start) %F A259751 a(n) = 12*n-2*(-1)^n-6. %F A259751 a(n) = a(n-1)+a(n-2)-a(n-3) for n>3. %F A259751 G.f.: 8*x*(1+x+x^2) / ((1-x)^2*(1+x)). %F A259751 (End) %F A259751 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/72. - _Amiram Eldar_, Dec 31 2021 %F A259751 E.g.f.: 2*(4 + (6*x - 3)*exp(x) - exp(-x)). - _David Lovler_, Sep 05 2022 %t A259751 A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]/# == 1/4 & ] %o A259751 (PARI) Vec(8*x*(1+x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Colin Barker_, Aug 26 2016 %Y A259751 Cf. A000914, A001651. %Y A259751 Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259749, A259750, A259752, A259754, A259755. %K A259751 nonn,easy %O A259751 1,1 %A A259751 _José María Grau Ribas_, Jul 06 2015 %E A259751 Better name from _Danny Rorabaugh_, Oct 22 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE