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Square root of A003462, rounded up.
1

%I #19 Jun 16 2022 10:24:53

%S 1,2,4,7,11,20,34,58,100,172,298,516,893,1547,2679,4640,8036,13918,

%T 24107,41754,72320,125262,216960,375786,650880,1127357,1952639,

%U 3382070,5857917,10146210,17573751,30438629,52721251,91315885,158163753,273947655,474491257,821842965

%N Square root of A003462, rounded up.

%C This sequence gives a lower bound for A090246. A003462 is the number of points in P(Z/3Z)^n. If a subset of P(Z/3Z)^n contains m points with no 3 collinear, then there are at most 2*C(m,2) points which are collinear with 2 points of the subset. Therefore if m + 2*C(m,2) = m^2 < A003462(n) we can add at least one more point to the set.

%H Chai Wah Wu, <a href="/A160393/b160393.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling(sqrt((3^n-1)/2)).

%o (PARI) a(n) = sqrtint((3^n-3)/2)+1; \\ _Michel Marcus_, Oct 20 2016; corrected Jun 15 2022

%Y Cf. A090246, A003462.

%K easy,nonn

%O 1,2

%A _Jack W Grahl_, May 12 2009