A047447 - OEIS

A047447

Numbers that are congruent to {2, 3, 5, 6} mod 8.

2, 3, 5, 6, 10, 11, 13, 14, 18, 19, 21, 22, 26, 27, 29, 30, 34, 35, 37, 38, 42, 43, 45, 46, 50, 51, 53, 54, 58, 59, 61, 62, 66, 67, 69, 70, 74, 75, 77, 78, 82, 83, 85, 86, 90, 91, 93, 94, 98, 99, 101, 102, 106, 107, 109, 110, 114, 115, 117, 118, 122, 123

(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 (1,0,0,1,-1).

FORMULA

G.f.: x*(2+x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

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

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (1+i)*(4*n-4*n*i+2*i-2-(1-i)*i^(2*n)+i^(1-n)-i^n)/4 where i=sqrt(-1).

a(2k) = A047398(k), a(2k-1) = A047617(k). (End)

E.g.f.: (4 + sin(x) - cos(x) + (4*x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016

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

MAPLE

A047447:=n->(1+I)*(4*n-4*n*I+2*I-2-(1-I)*I^(2*n)+I^(1-n)-I^n)/4: seq(A047447(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

MATHEMATICA

Table[(1+I)*(4n-4*n*I+2*I-2-(1-I)*I^(2n)+I^(1-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016

CROSSREFS

Cf. A047398, A047617.

Sequence in context: A303431 A317709 A034044 * A094739 A302494 A302534

Adjacent sequences: A047444 A047445 A047446 * A047448 A047449 A047450

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved