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A047494
Numbers that are congruent to {0, 1, 4, 5, 7} mod 8.
1
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
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
KEYWORD
nonn,easy
STATUS
approved