A047578 Numbers that are congruent to {2, 5, 6, 7} mod 8.

2, 5, 6, 7, 10, 13, 14, 15, 18, 21, 22, 23, 26, 29, 30, 31, 34, 37, 38, 39, 42, 45, 46, 47, 50, 53, 54, 55, 58, 61, 62, 63, 66, 69, 70, 71, 74, 77, 78, 79, 82, 85, 86, 87, 90, 93, 94, 95, 98, 101, 102, 103, 106, 109, 110, 111, 114, 117, 118, 119, 122, 125

Offset

1,1

Links

Table of n, a(n) for n=1..62.

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

Formula

G.f.: x*(1+x)*(x^2-x+2) / ((1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

a(n) = 2*n - cos(Pi*n/2). - Wesley Ivan Hurt, Oct 22 2013

From Wesley Ivan Hurt, May 20 2016: (Start)

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

a(n) = (4*n - i^(-n) - i^n)/2 where i=sqrt(-1).

a(2n) = A047550(n), a(2n-1) = A016825(n-1). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/8 - log(2)/4. - Amiram Eldar, Dec 26 2021

Maple

A047578:=n->2*n-cos(Pi*n/2): seq(A047578(n), n=1..100); # Wesley Ivan Hurt, Oct 22 2013

Mathematica

Flatten[#+{2, 5, 6, 7}&/@(8Range[0, 20])] (* Harvey P. Dale, Jan 26 2011 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n+2 for n in range(0, 56)] # Zerinvary Lajos, Jul 06 2008

Crossrefs

Cf. A016825, A047404, A047431, A047546, A047550, A056594.

Sequence in context: A285032 A002157 A050002 * A259605 A367695 A284393

Adjacent sequences: A047575 A047576 A047577 * A047579 A047580 A047581

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 20 2016

Status

approved