A047496 Numbers that are congruent to {0, 2, 4, 5, 7} mod 8.

0, 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 92, 93, 95, 96, 98, 100, 101, 103

Offset

1,2

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 + 1)*(x^3 + x^2 + 2)/((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 - 30 - 2*(n mod 5) + 3*((n+1) mod 5) - 2*((n+2) mod 5) - 2*((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-6, a(5k-4) = 8k-8. (End)

Maple

A047496:=n->8*floor(n/5)+[(0, 2, 4, 5, 7)][(n mod 5)+1]: seq(A047496(n), n=0..100); # Wesley Ivan Hurt, Jul 31 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 2, 4, 5, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 31 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 5, 7]]; // Wesley Ivan Hurt, Jul 31 2016

Crossrefs

Sequence in context: A020914 A195176 A195126 * A223735 A123663 A174131

Adjacent sequences: A047493 A047494 A047495 * A047497 A047498 A047499

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved