A047557 - OEIS

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A047557

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

4

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

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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