A259755 Numbers that are congruent to {4, 20} mod 24.

4, 20, 28, 44, 52, 68, 76, 92, 100, 116, 124, 140, 148, 164, 172, 188, 196, 212, 220, 236, 244, 260, 268, 284, 292, 308, 316, 332, 340, 356, 364, 380, 388, 404, 412, 428, 436, 452, 460, 476, 484, 500, 508, 524, 532, 548, 556, 572, 580, 596, 604, 620, 628

Offset

1,1

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

a(n) = 2*(6*n + (-1)^n - 3).

A259748(a(n))/a(n) = 3/4.

a(n) = 4*A007310(n). - Michel Marcus, Sep 22 2015

G.f.: 4*x*(1 + 4*x + x^2) / ((1 + x)*(1 - x)^2). - Bruno Berselli, Oct 23 2015

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

E.g.f.: 2*(2 + (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[200], Mod[A[#], #]/# == 3/4 &]
Table[2 (6 n + (-1)^n - 3), {n, 1, 60}] (* Bruno Berselli, Oct 23 2015 *)
LinearRecurrence[{1, 1, -1}, {4, 20, 28}, 60] (* Harvey P. Dale, Jul 19 2016 *)

Prog

(Magma) [2*(6*n+(-1)^n-3): n in [1..60]]; // Vincenzo Librandi, Aug 27 2015
(PARI) vector(100, n, 2*(6*n+(-1)^n-3)) \\ Altug Alkan, Oct 23 2015

Crossrefs

Cf. A000914, A007310.

Other sequences of numbers k such that A259748(k)/k equals a constant: A008606, A073762, A259749, A259750, A259751, A259752, A259754.

Sequence in context: A202070 A198831 A323040 * A317249 A181433 A079454

Adjacent sequences: A259752 A259753 A259754 * A259756 A259757 A259758

Keyword

nonn,easy

Author

José María Grau Ribas, Jul 18 2015

Extensions

Better name from Danny Rorabaugh, Oct 22 2015

Status

approved