A259751 Numbers that are congruent to {8, 16} mod 24.

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.

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Cf. A000914, A001651.

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

Adjacent sequences: A259748 A259749 A259750 * A259752 A259753 A259754

Keyword

nonn,easy

Author

José María Grau Ribas, Jul 06 2015

Extensions

Better name from Danny Rorabaugh, Oct 22 2015

Status

approved