A259750 Numbers that are congruent to {14, 22} mod 24.

14, 22, 38, 46, 62, 70, 86, 94, 110, 118, 134, 142, 158, 166, 182, 190, 206, 214, 230, 238, 254, 262, 278, 286, 302, 310, 326, 334, 350, 358, 374, 382, 398, 406, 422, 430, 446, 454, 470, 478, 494, 502, 518, 526, 542, 550, 566, 574, 590, 598, 614, 622, 638

Offset: 1

Author

José María Grau Ribas, Jul 04 2015

Keywords

• nonn
• easy

Comments

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

Links

• Danny Rorabaugh, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A000914, A168489, A259748.

Programs

Mathematica

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

PARI

vector(100, n, 2*(6*n-(-1)^n)) \\ Altug Alkan, Oct 23 2015

PARI

Vec(2*x*(7+4*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Aug 26 2016

Formula

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

a(n) = 2*A168489(n) - Danny Rorabaugh, Oct 22 2015

From Colin Barker, Aug 26 2016: (Start)

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

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

(End)

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

E.g.f.: 2*(1 + 6*x*exp(x) - exp(-x)). - David Lovler, Sep 06 2022

Extensions

Better name from Danny Rorabaugh, Oct 22 2015