A047546 - OEIS

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A047546

Numbers that are congruent to {2, 3, 4, 7} mod 8.

6

2, 3, 4, 7, 10, 11, 12, 15, 18, 19, 20, 23, 26, 27, 28, 31, 34, 35, 36, 39, 42, 43, 44, 47, 50, 51, 52, 55, 58, 59, 60, 63, 66, 67, 68, 71, 74, 75, 76, 79, 82, 83, 84, 87, 90, 91, 92, 95, 98, 99, 100, 103, 106, 107, 108, 111, 114, 115, 116, 119, 122, 123

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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

a(n) = A056594(n)+2*n-1. - Zerinvary Lajos, Jul 06 2008

a(n) = A047404(n)+1. - Zerinvary Lajos, Jul 06 2008

G.f.: x*(2-x+2*x^2+x^3) / ((1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

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-2+I^(1-n)+I^(n-1))/2 where I=sqrt(-1).

a(2n) = A004767(n-1) for n>0, a(2n-1) = A047463(n). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 3*Pi/16 - 3*log(2)/8. - Amiram Eldar, Dec 25 2021

MAPLE

A047546:=n->(4*n-2+I^(1-n)+I^(n-1))/2: seq(A047546(n), n=1..100); # Wesley Ivan Hurt, May 20 2016

MATHEMATICA

Table[(4n-2+I^(1-n)+I^(n-1))/2, {n, 80}] (* Wesley Ivan Hurt, May 20 2016 *)

PROG

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

(PARI) a(n)=(n-1)\4*8+[7, 2, 3, 4][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A004767, A047404, A047463, A056594.

Sequence in context: A080724 A342780 A089589 * A266530 A266510 A266540

Adjacent sequences: A047543 A047544 A047545 * A047547 A047548 A047549

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 20 2016

STATUS

approved