cp's OEIS Frontend

A181944 Number of convex quadrilaterals, distinct up to congruence, on an n X n grid (or geoboard).

%I A181944 #17 Feb 16 2025 08:33:13
%S A181944 0,1,12,89,407,1413,3894,9431,20212,39847,73177,127582,211012,337186,
%T A181944 519594,777447,1134269,1620415,2264873,3114709,4209184,5609209,
%U A181944 7378581,9594611,12326333,15688198,19779188,24721601,30646522,37727553,46093734,55983150,67558997
%N A181944 Number of convex quadrilaterals, distinct up to congruence, on an n X n grid (or geoboard).
%H A181944 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A181944.py">Python program</a>.
%H A181944 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConvexPolygon.html">Convex Polygon</a>.
%H A181944 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Quadrilateral.html">Quadrilateral</a>.
%e A181944 a(1) = 0 because the 1 X 1 grid has no quadrilaterals.
%e A181944 a(2) = 1 because the 2 X 2 grid has one quadrilateral.
%e A181944 a(3) = 9 because the 3 X 3 grid has 12 congruence classes of quadrilaterals, out of 70 quadrilaterals total:
%e A181944 +-------+-------+-------+-------+
%e A181944 | . . . | . o . | . . . | . o . |
%e A181944 | o o . | o . . | o . o | o . . |
%e A181944 | o o . | o o . | o . o | o . o |
%e A181944 +-------+-------+-------+-------+
%e A181944 | . . o | o . o | . o . | . o . |
%e A181944 | o . . | . . . | o o . | o . o |
%e A181944 | o . o | o . o | o . . | o . . |
%e A181944 +-------+-------+-------+-------+
%e A181944 | . o o | . . o | . o . | . . o |
%e A181944 | o . . | o . o | o . o | o . . |
%e A181944 | o . . | o . . | . o . | o o . |
%e A181944 +-------+-------+-------+-------+
%Y A181944 Cf. A189413.
%K A181944 nonn
%O A181944 1,3
%A A181944 _Martin Renner_, Apr 03 2012
%E A181944 a(7)-a(33) from _Lucas A. Brown_, Feb 06 2024