A047499 Numbers that are congruent to {3, 4, 5, 7} mod 8.

3, 4, 5, 7, 11, 12, 13, 15, 19, 20, 21, 23, 27, 28, 29, 31, 35, 36, 37, 39, 43, 44, 45, 47, 51, 52, 53, 55, 59, 60, 61, 63, 67, 68, 69, 71, 75, 76, 77, 79, 83, 84, 85, 87, 91, 92, 93, 95, 99, 100, 101, 103, 107, 108, 109, 111, 115, 116, 117, 119, 123, 124

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*(3+x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

From Wesley Ivan Hurt, May 27 2016: (Start)

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

a(n) = (8*n-1-i^(2*n)-(1-2*i)*i^(-n)-(1+2*i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047535(k), a(2k-1) = A047621(k). (End)

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

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 + (4-3*sqrt(2))*log(2)/16 + 3*sqrt(2)*log(2-sqrt(2))/8. - Amiram Eldar, Dec 26 2021

Maple

A047499:=n->(8*n-1-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047499(n), n=1..100); # Wesley Ivan Hurt, May 27 2016

Mathematica

Table[(8n-1-I^(2n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 7]]; // Wesley Ivan Hurt, May 27 2016

Crossrefs

Cf. A047535, A047621.

Sequence in context: A057773 A020486 A091428 * A330109 A082378 A046642

Adjacent sequences: A047496 A047497 A047498 * A047500 A047501 A047502

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved