A047510 Numbers that are congruent to {2, 4, 6, 7} mod 8.

2, 4, 6, 7, 10, 12, 14, 15, 18, 20, 22, 23, 26, 28, 30, 31, 34, 36, 38, 39, 42, 44, 46, 47, 50, 52, 54, 55, 58, 60, 62, 63, 66, 68, 70, 71, 74, 76, 78, 79, 82, 84, 86, 87, 90, 92, 94, 95, 98, 100, 102, 103, 106, 108, 110, 111, 114, 116, 118, 119, 122, 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

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

G.f.: x*(2+2*x+2*x^2+x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).

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

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

a(2k) = A047535(k), a(2k-1) = A016825(k-1) for k>0. (End)

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

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

Maple

A047510:=n->(8*n-1-I^(2*n)-I^(-n)-I^n)/4: seq(A047510(n), n=1..100); # Wesley Ivan Hurt, May 27 2016

Mathematica

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

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016

Crossrefs

Cf. A016825, A047535.

Sequence in context: A286047 A325426 A227090 * A189030 A198033 A375598

Adjacent sequences: A047507 A047508 A047509 * A047511 A047512 A047513

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved