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Smallest mode of the sequences n/(n-k)*binomial(n,n-k) (see link).
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%I #13 Sep 08 2022 08:45:11

%S 0,1,1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,6,7,7,7,8,8,8,8,9,9,9,9,

%T 10,10,10,11,11,11,11,12,12,12,13,13,13,13,14,14,14,14,15,15,15,16,16,

%U 16,16,17,17,17,18,18,18,18,19,19,19,19,20,20,20,21,21,21,21,22,22,22,22

%N Smallest mode of the sequences n/(n-k)*binomial(n,n-k) (see link).

%H Moussa Benoumhani, <a href="http://www.cs.uwaterloo.ca/journals/JIS//VOL6/Benoumhani/benoumhani8.html">A Sequence of Binomial Coefficients Related to Lucas and Fibonacci Numbers</a>, J. Integer Seqs., Vol. 6, 2003, Article 03.2.1.

%F a(n) = ceiling(1/10*(5*n-4-sqrt(5*n^2-4))).

%t Table[Ceiling[1/10 (5 n - 4 - Sqrt[5 n^2 - 4])], {n, 1, 100}] (* _Vincenzo Librandi_, May 21 2015 *)

%o (PARI) vector(80, n, ceil(1/10*(5*n-4-sqrt(5*n^2-4)))) \\ _Michel Marcus_, May 20 2015

%o (Magma) [Ceiling(1/10*(5*n-4-Sqrt(5*n^2-4))): n in [1..100]]; // _Vincenzo Librandi_, May 21 2015

%K nonn

%O 1,6

%A _Benoit Cloitre_, Jul 28 2003