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A047453
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Numbers that are congruent to {0, 1, 2, 3, 4} mod 8.
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1
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0, 1, 2, 3, 4, 8, 9, 10, 11, 12, 16, 17, 18, 19, 20, 24, 25, 26, 27, 28, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 56, 57, 58, 59, 60, 64, 65, 66, 67, 68, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 88, 89, 90, 91, 92, 96, 97, 98, 99, 100, 104
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: x^2*(1+x+x^2+x^3+4*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011
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 - 70 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 12*((n+4) mod 5))/25.
a(5k) = 8k-4, a(5k-1) = 8k-5, a(5k-2) = 8k-6, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)
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MAPLE
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MATHEMATICA
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Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 8}, 80] (* Harvey P. Dale, Jul 04 2015 *)
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PROG
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(Magma) [n : n in [0..150] | n mod 8 in [0..4]]; // Wesley Ivan Hurt, Jul 31 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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