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A306755
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a(n) = a(n-6) + a(n-7) with a(0)=7, a(1)=...=a(5)=0, a(6)=6.
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2
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7, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 6, 13, 7, 0, 0, 0, 6, 19, 20, 7, 0, 0, 6, 25, 39, 27, 7, 0, 6, 31, 64, 66, 34, 7, 6, 37, 95, 130, 100, 41, 13, 43, 132, 225, 230, 141, 54, 56, 175, 357, 455, 371, 195, 110, 231, 532, 812, 826, 566, 305, 341, 763, 1344, 1638, 1392, 871, 646, 1104, 2107
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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.: (7 - x^6)/(1 - x^6 - x^7).
a(0) = 7 and a(n) = n*Sum_{k=1..floor(n/6)} binomial(k,n-6*k)/k for n > 0.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 1, 1}, {7, 0, 0, 0, 0, 0, 6}, 100] (* Amiram Eldar, Jun 21 2021 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec((7-x^6)/(1-x^6-x^7))
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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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