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A259751
Numbers that are congruent to {8, 16} mod 24.
6
8, 16, 32, 40, 56, 64, 80, 88, 104, 112, 128, 136, 152, 160, 176, 184, 200, 208, 224, 232, 248, 256, 272, 280, 296, 304, 320, 328, 344, 352, 368, 376, 392, 400, 416, 424, 440, 448, 464, 472, 488, 496, 512, 520, 536, 544, 560, 568, 584, 592, 608, 616, 632
OFFSET
1,1
COMMENTS
Original name: Numbers n such that n/A259748(n) = 4.
FORMULA
A259748(a(n))/a(n) = 1/4.
a(n) = 8*A001651. - Danny Rorabaugh, Oct 22 2015
From Colin Barker, Aug 26 2016: (Start)
a(n) = 12*n-2*(-1)^n-6.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
G.f.: 8*x*(1+x+x^2) / ((1-x)^2*(1+x)).
(End)
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/72. - Amiram Eldar, Dec 31 2021
E.g.f.: 2*(4 + (6*x - 3)*exp(x) - exp(-x)). - David Lovler, Sep 05 2022
MATHEMATICA
A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]/# == 1/4 & ]
PROG
(PARI) Vec(8*x*(1+x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Aug 26 2016
CROSSREFS
Other sequences of numbers n such that A259748(n)/n equals a constant: A008606, A073762, A259749, A259750, A259752, A259754, A259755.
Sequence in context: A285315 A020948 A219547 * A106841 A260711 A139598
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Better name from Danny Rorabaugh, Oct 22 2015
STATUS
approved