A047542 Numbers that are congruent to {0, 1, 2, 4, 7} mod 8.

0, 1, 2, 4, 7, 8, 9, 10, 12, 15, 16, 17, 18, 20, 23, 24, 25, 26, 28, 31, 32, 33, 34, 36, 39, 40, 41, 42, 44, 47, 48, 49, 50, 52, 55, 56, 57, 58, 60, 63, 64, 65, 66, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 84, 87, 88, 89, 90, 92, 95, 96, 97, 98, 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 + 2*x^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 - 50 - 7*(n mod 5) - 2*((n+1) mod 5) + 3*((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-6, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)

Maple

A047542:=n->8*floor(n/5)+[(0, 1, 2, 4, 7)][(n mod 5)+1]: seq(A047542(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 4, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 28 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 4, 7, 8}, 80] (* Harvey P. Dale, Jan 27 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 4, 7]]; // Wesley Ivan Hurt, Jul 28 2016

Crossrefs

Sequence in context: A103254 A299419 A083454 * A121619 A167500 A010377

Adjacent sequences: A047539 A047540 A047541 * A047543 A047544 A047545

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved