A047597 Numbers that are congruent to {0, 2, 3, 4, 5} mod 8.

0, 2, 3, 4, 5, 8, 10, 11, 12, 13, 16, 18, 19, 20, 21, 24, 26, 27, 28, 29, 32, 34, 35, 36, 37, 40, 42, 43, 44, 45, 48, 50, 51, 52, 53, 56, 58, 59, 60, 61, 64, 66, 67, 68, 69, 72, 74, 75, 76, 77, 80, 82, 83, 84, 85, 88, 90, 91, 92, 93, 96, 98, 99, 100, 101

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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

Formula

From Chai Wah Wu, Jun 10 2016: (Start)

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

G.f.: x^2*(3*x^4 + x^3 + x^2 + x + 2)/(x^6 - x^5 - x + 1). (End)

From Wesley Ivan Hurt, Jul 28 2016: (Start)

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

a(n) = (40*n - 50 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) - 7*((n+4) mod 5))/25.

a(5k) = 8k-3, a(5k-1) = 8k-4, a(5k-2) = 8k-5, a(5k-3) = 8k-6, a(5k-4) = 8k-8. (End)

Maple

A047597:=n->8*floor(n/5)+[(0, 2, 3, 4, 5)][(n mod 5)+1]: seq(A047597(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 3, 4, 5}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 28 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 2, 3, 4, 5, 8}, 70] (* Harvey P. Dale, Dec 15 2019 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 4, 5]]; // Wesley Ivan Hurt, Jul 28 2016

Crossrefs

Sequence in context: A056804 A305399 A101547 * A309960 A247935 A005233

Adjacent sequences: A047594 A047595 A047596 * A047598 A047599 A047600

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved