A047494 Numbers that are congruent to {0, 1, 4, 5, 7} mod 8.

0, 1, 4, 5, 7, 8, 9, 12, 13, 15, 16, 17, 20, 21, 23, 24, 25, 28, 29, 31, 32, 33, 36, 37, 39, 40, 41, 44, 45, 47, 48, 49, 52, 53, 55, 56, 57, 60, 61, 63, 64, 65, 68, 69, 71, 72, 73, 76, 77, 79, 80, 81, 84, 85, 87, 88, 89, 92, 93, 95, 96, 97, 100, 101, 103

Offset

1,3

Links

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

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

Formula

G.f.: x^2*(x^4+2*x^3+x^2+3*x+1)/((x-1)^2*(x^4+x^3+x^2+x+1)). [Colin Barker, Jun 22 2012]

From Wesley Ivan Hurt, Jul 31 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 35 - 2*(n mod 5) + 3*((n+1) mod 5) - 7*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

a(5k) = 8k-1, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)

Maple

A047494:=n->8*floor(n/5)+[(0, 1, 4, 5, 7)][(n mod 5)+1]: seq(A047494(n), n=0..100); # Wesley Ivan Hurt, Jul 31 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 31 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 4, 5, 7, 8}, 80] (* Harvey P. Dale, Jul 02 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 4, 5, 7]]; // Wesley Ivan Hurt, Jul 31 2016

Crossrefs

Sequence in context: A298874 A266267 A189477 * A080712 A005048 A119642

Adjacent sequences: A047491 A047492 A047493 * A047495 A047496 A047497

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved