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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

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 *)

Sage

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

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

Extensions

More terms from Wesley Ivan Hurt, May 20 2016