A047404 Numbers that are congruent to {1, 2, 3, 6} mod 8.

1, 2, 3, 6, 9, 10, 11, 14, 17, 18, 19, 22, 25, 26, 27, 30, 33, 34, 35, 38, 41, 42, 43, 46, 49, 50, 51, 54, 57, 58, 59, 62, 65, 66, 67, 70, 73, 74, 75, 78, 81, 82, 83, 86, 89, 90, 91, 94, 97, 98, 99, 102, 105, 106, 107, 110, 113, 114, 115, 118, 121, 122, 123

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

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

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

From Wesley Ivan Hurt, May 30 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-4+i^(1-n)-i^(1+n))/2 where i = sqrt(-1).

a(2k) = A016825(k-1) k>0, a(2k-1) = A047471(k). (End)

E.g.f.: 2 + sin(x) + 2*(x - 1)*exp(x). - Ilya Gutkovskiy, May 30 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/8 + log(2)/4. - Amiram Eldar, Dec 23 2021

Maple

A047404:=n->(4*n-4+I^(1-n)-I^(1+n))/2: seq(A047404(n), n=1..100); # Wesley Ivan Hurt, May 30 2016

Mathematica

Table[(4n-4+I^(1-n)-I^(1+n))/2, {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *)

Prog

(Sage) [lucas_number1(n, 0, 1)+2*n-2 for n in range(1, 56)] # Zerinvary Lajos, Jul 06 2008
(PARI) a(n)=(n-1)\4*8+[6, 1, 2, 3][n%4+1] \\ Charles R Greathouse IV, Jun 11 2015
(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 3, 6]]; // Wesley Ivan Hurt, May 30 2016

Crossrefs

Cf. A016825, A047471, A056594.

Sequence in context: A061910 A344208 A007086 * A133555 A328727 A032938

Adjacent sequences: A047401 A047402 A047403 * A047405 A047406 A047407

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved