A160393 Square root of A003462, rounded up.

1, 2, 4, 7, 11, 20, 34, 58, 100, 172, 298, 516, 893, 1547, 2679, 4640, 8036, 13918, 24107, 41754, 72320, 125262, 216960, 375786, 650880, 1127357, 1952639, 3382070, 5857917, 10146210, 17573751, 30438629, 52721251, 91315885, 158163753, 273947655, 474491257, 821842965

Offset: 1

Author

Jack W Grahl, May 12 2009

Keywords

• easy
• nonn

Comments

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.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A090246, A003462.

Programs

PARI

a(n) = sqrtint((3^n-3)/2)+1; \\ Michel Marcus, Oct 20 2016; corrected Jun 15 2022

Formula

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