A047574 Numbers that are congruent to {5, 6, 7} mod 8.

5, 6, 7, 13, 14, 15, 21, 22, 23, 29, 30, 31, 37, 38, 39, 45, 46, 47, 53, 54, 55, 61, 62, 63, 69, 70, 71, 77, 78, 79, 85, 86, 87, 93, 94, 95, 101, 102, 103, 109, 110, 111, 117, 118, 119, 125, 126, 127, 133, 134, 135, 141, 142, 143, 149, 150, 151, 157, 158, 159

Offset

1,1

Links

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

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

Formula

From Chai Wah Wu, May 30 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

G.f.: x*(x^3 + x^2 + x + 5)/(x^4 - x^3 - x + 1). (End)

a(n) = (8*n-10*sin(2*Pi*(n+1)/3)/sqrt(3)+2)/3. - Ilya Gutkovskiy, May 30 2016

a(n) = 8*floor((n-1)/3)+((n-1) mod 3)+5. - David A. Corneth, May 30 2016

a(3k) = 8k-1, a(3k-1) = 8k-2, a(3k-2) = 8k-3. - Wesley Ivan Hurt, Jun 10 2016

Maple

A047574:=n->8*floor((n-1)/3)+((n-1) mod 3)+5: seq(A047574(n), n=1..100); # Wesley Ivan Hurt, Jun 10 2016

Mathematica

Select[Range[200], MemberQ[{5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 30 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {5, 6, 7, 13}, 60] (* Harvey P. Dale, Jul 29 2016 *)

Prog

(Magma) [n: n in [0..200] | n mod 8 in [5..7]]; // Vincenzo Librandi, May 30 2016
(PARI) a(n)=8 * (n-1)\3 + (n-1)%3 + 5 \\ David A. Corneth, May 30 2016

Crossrefs

Sequence in context: A327106 A003273 A006991 * A273929 A067531 A031029

Adjacent sequences: A047571 A047572 A047573 * A047575 A047576 A047577

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved