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A047542
Numbers that are congruent to {0, 1, 2, 4, 7} mod 8.
1
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
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
KEYWORD
nonn,easy
STATUS
approved