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A047578 Numbers that are congruent to {2, 5, 6, 7} mod 8. 4
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 (list; graph; refs; listen; history; text; internal format)
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)

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 xrange(0, 56)] # Zerinvary Lajos, Jul 06 2008

CROSSREFS

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

Sequence in context: A285032 A002157 A050002 * A259605 A284393 A287366

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

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Last modified February 23 12:35 EST 2019. Contains 320431 sequences. (Running on oeis4.)