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URL: https://oeis.org/A306758

⇱ A306758 - OEIS

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A306758
a(n) = a(n-9) + a(n-10) with a(0)=10, a(1)=...=a(8)=0, a(9)=9.
2
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
OFFSET
0,1
COMMENTS
Conjecture: If p is prime, p divides a(p).
FORMULA
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.
MATHEMATICA
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 *)
PROG
(PARI) N=99; x='x+O('x^N); Vec((10-x^9)/(1-x^9-x^10))
CROSSREFS
Column 9 of A306646.
Sequence in context: A285476 A270035 A228636 * A340983 A247118 A010894
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 08 2019
STATUS
approved