A047576 Numbers that are congruent to {1, 5, 6, 7} mod 8.

1, 5, 6, 7, 9, 13, 14, 15, 17, 21, 22, 23, 25, 29, 30, 31, 33, 37, 38, 39, 41, 45, 46, 47, 49, 53, 54, 55, 57, 61, 62, 63, 65, 69, 70, 71, 73, 77, 78, 79, 81, 85, 86, 87, 89, 93, 94, 95, 97, 101, 102, 103, 105, 109, 110, 111, 113, 117, 118, 119, 121, 125

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

From Wesley Ivan Hurt, May 29 2016: (Start)

G.f.: x*(1+4*x+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)-(2+i)*i^(-n)-(2-i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047550(k), a(2k-1) = A047452(k). (End)

E.g.f.: (2 - sin(x) - 2*cos(x) - sinh(x) + 4*x*exp(x))/2. - Ilya Gutkovskiy, May 30 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = 3*sqrt(2)*Pi/16 - (sqrt(2)+2)*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 24 2021

Maple

A047576:=n->(8*n-1+I^(2*n)-(2+I)*I^(-n)-(2-I)*I^n)/4: seq(A047576(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Flatten[#+{1, 5, 6, 7}&/@(8Range[0, 20])] (* Harvey P. Dale, Apr 22 2011 *)
Select[Range[100], MemberQ[{1, 5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 30 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 5, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047452, A047550.

Sequence in context: A241203 A279001 A080708 * A123123 A308892 A092858

Adjacent sequences: A047573 A047574 A047575 * A047577 A047578 A047579

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved