A092259 Numbers that are congruent to {4, 8} mod 12.

4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92, 100, 104, 112, 116, 124, 128, 136, 140, 148, 152, 160, 164, 172, 176, 184, 188, 196, 200, 208, 212, 220, 224, 232, 236, 244, 248, 256, 260, 268, 272, 280, 284, 292, 296, 304, 308, 316, 320, 328, 332

Offset

1,1

Links

Table of n, a(n) for n=1..56.

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

Formula

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

a(n) = 4 * A001651(n).

Iff phi(n) = phi(3n/2), then n is in A069587. - Labos Elemer, Feb 25 2004

a(n) = 12*(n-1)-a(n-1) (with a(1)=4). - Vincenzo Librandi, Nov 16 2010

From Wesley Ivan Hurt, May 21 2016: (Start)

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

a(n) = 6n - 3 - (-1)^n.

a(2n) = A017617(n-1) for n>1, a(2n-1) = A017569(n-1) for n>1.

a(n) = -a(1-n), a(n) = A092899(n) + 1 for n>0. (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*sqrt(3)/36. - Amiram Eldar, Dec 30 2021

Maple

A092259:=n->6*n-3-(-1)^n: seq(A092259(n), n=1..100); # Wesley Ivan Hurt, May 21 2016

Mathematica

Table[6n-3-(-1)^n, {n, 80}] (* Wesley Ivan Hurt, May 21 2016 *)
LinearRecurrence[{1, 1, -1}, {4, 8, 16}, 60] (* Harvey P. Dale, Oct 07 2021 *)

Prog

(Magma) [n : n in [0..400] | n mod 12 in [4, 8]]; // Wesley Ivan Hurt, May 21 2016

Crossrefs

Cf. A001651, A017617, A017569, A069587, A092899.

Fourth row of A092260.

Sequence in context: A312803 A312804 A306199 * A312805 A312806 A036693

Adjacent sequences: A092256 A092257 A092258 * A092260 A092261 A092262

Keyword

nonn,easy

Author

Giovanni Teofilatto, Feb 19 2004

Extensions

Edited and extended by Ray Chandler, Feb 21 2004

Status

approved