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A306758
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a(n) = a(n-9) + a(n-10) with a(0)=10, a(1)=...=a(8)=0, a(9)=9.
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2
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10, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 0, 0, 0, 0, 0, 0, 0, 9, 19, 10, 0, 0, 0, 0, 0, 0, 9, 28, 29, 10, 0, 0, 0, 0, 0, 9, 37, 57, 39, 10, 0, 0, 0, 0, 9, 46, 94, 96, 49, 10, 0, 0, 0, 9, 55, 140, 190, 145, 59, 10, 0, 0, 9, 64, 195, 330, 335, 204, 69, 10, 0, 9, 73, 259, 525, 665
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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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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1,1).
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FORMULA
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G.f.: (10 - x^9)/(1 - x^9 - x^10).
a(0) = 10 and a(n) = n*Sum_{k=1..floor(n/9)} binomial(k,n-9*k)/k for n > 0.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 1, 1}, {10, 0, 0, 0, 0, 0, 0, 0, 0, 9}, 80] (* Harvey P. Dale, Jan 18 2021 *)
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PROG
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(PARI) N=99; x='x+O('x^N); Vec((10-x^9)/(1-x^9-x^10))
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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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