A047557 Numbers that are congruent to {0, 3, 6, 7} mod 8.

0, 3, 6, 7, 8, 11, 14, 15, 16, 19, 22, 23, 24, 27, 30, 31, 32, 35, 38, 39, 40, 43, 46, 47, 48, 51, 54, 55, 56, 59, 62, 63, 64, 67, 70, 71, 72, 75, 78, 79, 80, 83, 86, 87, 88, 91, 94, 95, 96, 99, 102, 103, 104, 107, 110, 111, 112, 115, 118, 119, 120, 123, 126

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+x^2) / ( (x^2+1)*(x-1)^2 ).

a(n) = 2*n-1-sin(Pi*n/2). (End)

a(n) = 2n-1-cos(Pi*(n-1)/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) = 2*n-2-I^(1-n)*(I^(n-1)-1)^2/2 where I=sqrt(-1).

a(2n) = A004767(n-1) for n>0, a(2n-1) = A047451(n). (End)

Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 - Pi/16. - Amiram Eldar, Dec 23 2021

Maple

A047557:=n->2*n-1-cos(Pi*(n-1)/2): seq(A047557(k), k=1..100); # Wesley Ivan Hurt, Oct 22 2013

Mathematica

Table[2n-1-Cos[Pi(n-1)/2], {n, 100}] (* Wesley Ivan Hurt, Oct 22 2013 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n+3 for n in range(-1, 55)] # Zerinvary Lajos, Jul 06 2008

Crossrefs

Cf. A004767, A047404, A047431, A047451, A047546, A047578, A056594.

Sequence in context: A347878 A289176 A277851 * A342736 A284390 A099850

Adjacent sequences: A047554 A047555 A047556 * A047558 A047559 A047560

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 20 2016

Status

approved