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A306756
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a(n) = a(n-7) + a(n-8) with a(0)=8, a(1)=...=a(6)=0, a(7)=7.
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2
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8, 0, 0, 0, 0, 0, 0, 7, 8, 0, 0, 0, 0, 0, 7, 15, 8, 0, 0, 0, 0, 7, 22, 23, 8, 0, 0, 0, 7, 29, 45, 31, 8, 0, 0, 7, 36, 74, 76, 39, 8, 0, 7, 43, 110, 150, 115, 47, 8, 7, 50, 153, 260, 265, 162, 55, 15, 57, 203, 413, 525, 427, 217, 70, 72, 260, 616, 938, 952, 644, 287, 142
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OFFSET
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0,1
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COMMENTS
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Conjecture: If p is prime, p divides a(p).
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LINKS
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FORMULA
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G.f.: (8 - x^7)/(1 - x^7 - x^8).
a(0) = 8 and a(n) = n*Sum_{k=1..floor(n/7)} binomial(k,n-7*k)/k for n > 0.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1}, {8, 0, 0, 0, 0, 0, 0, 7}, 100] (* Amiram Eldar, Jun 21 2021 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec((8-x^7)/(1-x^7-x^8))
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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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