A047545 Numbers that are congruent to {0, 1, 3, 4, 7} mod 8.

0, 1, 3, 4, 7, 8, 9, 11, 12, 15, 16, 17, 19, 20, 23, 24, 25, 27, 28, 31, 32, 33, 35, 36, 39, 40, 41, 43, 44, 47, 48, 49, 51, 52, 55, 56, 57, 59, 60, 63, 64, 65, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 84, 87, 88, 89, 91, 92, 95, 96, 97, 99, 100, 103, 104

Offset

1,3

Links

Table of n, a(n) for n=1..66.

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*(x^4 + 3*x^3 + x^2 + 2*x + 1)/(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 - 45 - 7*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) + 3*((n+4) mod 5))/25.

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

Maple

A047545:=n->8*floor(n/5)+[(0, 1, 3, 4, 7)][(n mod 5)+1]: seq(A047545(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Flatten[#+{0, 1, 3, 4, 7}&/@(8 Range[0, 11])] (* Harvey P. Dale, Jan 18 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 3, 4, 7]]; // Wesley Ivan Hurt, Jul 28 2016

Crossrefs

Sequence in context: A100991 A075821 A120515 * A296352 A192052 A187230

Adjacent sequences: A047542 A047543 A047544 * A047546 A047547 A047548

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved