A047558 Numbers that are congruent to {1, 3, 6, 7} mod 8.

1, 3, 6, 7, 9, 11, 14, 15, 17, 19, 22, 23, 25, 27, 30, 31, 33, 35, 38, 39, 41, 43, 46, 47, 49, 51, 54, 55, 57, 59, 62, 63, 65, 67, 70, 71, 73, 75, 78, 79, 81, 83, 86, 87, 89, 91, 94, 95, 97, 99, 102, 103, 105, 107, 110, 111, 113, 115, 118, 119, 121, 123, 126

Offset

1,2

Links

Table of n, a(n) for n=1..63.

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+2*x+3*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-3-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).

a(2k) = A004767(k-1) for k>0, a(2k-1) = A047452(k). (End)

E.g.f.: (2 - sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 30 2016

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

Maple

A047558:=n->(8*n-3-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047558(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Select[Range[150], MemberQ[{1, 3, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jul 31 2014 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A004767, A047452.

Sequence in context: A026406 A289182 A188974 * A160217 A228014 A188971

Adjacent sequences: A047555 A047556 A047557 * A047559 A047560 A047561

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved