A133265 Diagonal of the A135356 triangle.

2, 2, 2, 4, 2, 6, 2, 8, 2, 10, 2, 12, 2, 14, 2, 16, 2, 18, 2, 20, 2, 22, 2, 24, 2, 26, 2, 28, 2, 30, 2, 32, 2, 34, 2, 36, 2, 38, 2, 40, 2, 42, 2, 44, 2, 46, 2, 48, 2, 50, 2, 52, 2, 54, 2, 56, 2, 58, 2, 60, 2, 62, 2, 64, 2, 66, 2, 68, 2, 70, 2, 72, 2, 74, 2, 76, 2, 78, 2, 80

Offset

0,1

Comments

Regular continued fraction expansion of 2*sin(1/2)/( cos(1/2) - sin(1/2) ) = 2.40822 34423 35827 84841 ... = 2 + 1/(2 + 1/(2 + 1/(4 + 1/(2 + 1/(6 + 1/(2 + 1/(8 + 1/(2 + ... )))))))). Cf. A019425. - Peter Bala, Feb 15 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

2*(A057979 without 1, 0, first two terms).

a(n) = (n+3+(n-1)*(-1)^(n+1))/2. - Vincenzo Librandi, Aug 30 2011

a(n) = (2*n + 5) mod (n*(3 + (-1)^n) - (-1)^n + 7)/2. - Lechoslaw Ratajczak, Nov 17 2016

From Colin Barker, Nov 17 2016: (Start)

a(n) = 2*a(n-2) - a(n-4) for n>3.

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

(End)

Maple

A133265 := n -> (n+2+(n-2)*(-1)^n)/2: # Peter Luschny, Aug 30 2011

Mathematica

Table[(n + 3 + (n - 1) (-1)^(n + 1))/2, {n, 0, 79}] (* or *)
Table[Mod[(2 n + 5), (n (3 + (-1)^n) - (-1)^n + 7)/2], {n, 0, 79}] (* or *)
CoefficientList[Series[2 (1 + x - x^2)/((1 - x)^2*(1 + x)^2), {x, 0, 79}], x] (* Michael De Vlieger, Nov 18 2016 *)

Prog

(Magma) [(n+3+(n-1)*(-1)^(n+1))/2: n in [0..80]]; // Vincenzo Librandi, Aug 30 2011
(PARI) Vec(2*(1 + x - x^2) / ((1 - x)^2 * (1 + x)^2) + O(x^100)) \\ Colin Barker, Nov 17 2016

Crossrefs

Cf. A019425.

Sequence in context: A349483 A114349 A186749 * A298076 A054712 A345067

Adjacent sequences: A133262 A133263 A133264 * A133266 A133267 A133268

Keyword

nonn,easy

Author

Paul Curtz, Dec 20 2007

Status

approved