A047444 Numbers that are congruent to {0, 3, 5, 6} mod 8.

0, 3, 5, 6, 8, 11, 13, 14, 16, 19, 21, 22, 24, 27, 29, 30, 32, 35, 37, 38, 40, 43, 45, 46, 48, 51, 53, 54, 56, 59, 61, 62, 64, 67, 69, 70, 72, 75, 77, 78, 80, 83, 85, 86, 88, 91, 93, 94, 96, 99, 101, 102, 104, 107, 109, 110, 112, 115, 117, 118, 120, 123, 125

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

G.f.: x^2*(3-x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, May 26 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(n) = (1+i)*(4*n-4*n*i+3*i-3-i^(-n)+i^(1+n))/4 where i=sqrt(-1).

a(2k) = A047398(k), a(2k-1) = A047645(k). (End)

E.g.f.: (4 - sin(x) - cos(x) + (4*x - 3)*exp(x))/2. - Ilya Gutkovskiy, May 27 2016

Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/8 - (3-2*sqrt(2))*Pi/16. - Amiram Eldar, Dec 21 2021

Maple

A047444:=n->(1+I)*(4*n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4: seq(A047444(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

Mathematica

Table[(1+I)*(4n-4*n*I+3*I-3-I^(-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
LinearRecurrence[{2, -2, 2, -1}, {0, 3, 5, 6}, 70] (* Harvey P. Dale, Aug 26 2019 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016

Crossrefs

Cf. A047398, A047645.

Sequence in context: A087720 A309544 A154111 * A279933 A327206 A212439

Adjacent sequences: A047441 A047442 A047443 * A047445 A047446 A047447

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved