caa a22 4500 445868929 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00605-010-0236-6 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0236-6 Formulas for the number of gridlines [Elektronische Daten] [Anne-Maria Ernvall-Hytönen, Kaisa Matomäki, Pentti Haukkanen, Jorma Merikoski] Let l(n) be the number of lines through at least two points of an n× n rectangular grid. We prove recursive and asymptotic formulas for it using respectively combinatorial and number theoretic methods. We also study the ratio l(n)/l(n − 1). All this originates from Mustonen's experimental results. Springer-Verlag, 2010 Rectangular grid nationallicence Lattice points nationallicence Euler $${\phi}$$-function nationallicence Asymptotic formulas nationallicence Recursive formulas nationallicence Ernvall-Hytönen Anne-Maria Institutionen för matematik, Kungliga Tekniska Högskolan, 100 44, Stockholm, Sweden aut Matomäki Kaisa Department of Mathematics, University of Turku, 20014, Turku, Finland aut Haukkanen Pentti Department of Mathematics and Statistics, University of Tampere, 33014, Tampere, Finland aut Merikoski Jorma Department of Mathematics and Statistics, University of Tampere, 33014, Tampere, Finland aut Monatshefte für Mathematik Springer Vienna 164/2(2011-10-01), 157-170 0026-9255 164:2<157 2011 164 605 https://doi.org/10.1007/s00605-010-0236-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0236-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ernvall-Hytönen Anne-Maria Institutionen för matematik, Kungliga Tekniska Högskolan, 100 44, Stockholm, Sweden aut NATIONALLICENCE 700 1- Matomäki Kaisa Department of Mathematics, University of Turku, 20014, Turku, Finland aut NATIONALLICENCE 700 1- Haukkanen Pentti Department of Mathematics and Statistics, University of Tampere, 33014, Tampere, Finland aut NATIONALLICENCE 700 1- Merikoski Jorma Department of Mathematics and Statistics, University of Tampere, 33014, Tampere, Finland aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/2(2011-10-01), 157-170 0026-9255 164:2<157 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer