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

1,1

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).

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000914, A168489, A259748.

Sequence in context: A225710 A183185 A324526 * A211416 A045282 A039291

Adjacent sequences: A259747 A259748 A259749 * A259751 A259752 A259753

Keyword

nonn,easy

Author

José María Grau Ribas, Jul 04 2015

Extensions

Better name from Danny Rorabaugh, Oct 22 2015

Status

approved