A047599 Numbers that are congruent to {0, 3, 4, 5} mod 8.

0, 3, 4, 5, 8, 11, 12, 13, 16, 19, 20, 21, 24, 27, 28, 29, 32, 35, 36, 37, 40, 43, 44, 45, 48, 51, 52, 53, 56, 59, 60, 61, 64, 67, 68, 69, 72, 75, 76, 77, 80, 83, 84, 85, 88, 91, 92, 93, 96, 99, 100, 101, 104, 107, 108, 109, 112, 115, 116, 117, 120, 123, 124

Offset

1,2

Links

Table of n, a(n) for n=1..63.

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

Formula

From R. J. Mathar, Oct 08 2011: (Start)

G.f.: ( x^2*(3-2*x+3*x^2) ) / ( (x^2+1)*(x-1)^2 ).

a(n) = 2*n-2-cos(n*Pi/2). (End)

From Wesley Ivan Hurt, May 22 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(n) = 2n - 2 - (i^(-n) + i^n)/2 where i = sqrt(-1).

a(2n) = A047621(n), a(2n+1) = A008586(n) for n>0. (End)

Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/4 + sqrt(2)*log(3-2*sqrt(2))/8. - Amiram Eldar, Dec 21 2021

Maple

A047599:=n->2*n-2-(I^(-n)+I^n)/2: seq(A047599(n), n=1..100); # Wesley Ivan Hurt, May 22 2016

Mathematica

Table[2n-2-(I^(-n)+I^n)/2, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {0, 3, 4, 5}, 80] (* Harvey P. Dale, Mar 27 2023 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n for n in range(0, 55)] # Zerinvary Lajos, Mar 09 2009
(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4, 5]]; // Wesley Ivan Hurt, May 22 2016

Crossrefs

Cf. A008586, A047621.

Sequence in context: A080726 A101210 A206445 * A332414 A050846 A035538

Adjacent sequences: A047596 A047597 A047598 * A047600 A047601 A047602

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 22 2016

Status

approved