cp's OEIS Frontend

A181945 Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).

%I A181945 #26 Feb 16 2025 08:33:13
%S A181945 0,1,9,43,141,343,766,1415,2517,4129,6545,9505,14230,19444,26733,
%T A181945 36208,48029,60675,78729,96866,122433,151288,184072,217998,266775,
%U A181945 315096,371138,435153,512549,585240,688470,779196,895058,1019697,1153081,1305629,1494185,1656287
%N A181945 Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).
%H A181945 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A181945.py">Python program</a>.
%H A181945 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Trapezoid.html">Trapezoid</a>.
%e A181945 a(1) = 0 because the 1 X 1 grid has no trapezoids.
%e A181945 a(2) = 1 because the 2 X 2 grid has one trapezoid.
%e A181945 a(3) = 9 because the 3 X 3 grid has 9 congruence classes of trapezoids, out of 50 trapezoids total:
%e A181945 +-------+-------+-------+
%e A181945 | . . . | . o . | . . . |
%e A181945 | o o . | o . . | o . o |
%e A181945 | o o . | o o . | o . o |
%e A181945 +-------+-------+-------+
%e A181945 | . . o | o . o | . o . |
%e A181945 | o . . | . . . | o o . |
%e A181945 | o . o | o . o | o . . |
%e A181945 +-------+-------+-------+
%e A181945 | . o o | . . o | . o . |
%e A181945 | o . . | o . o | o . o |
%e A181945 | o . . | o . . | . o . |
%e A181945 +-------+-------+-------+
%Y A181945 Cf. A181944, A189415.
%K A181945 nonn
%O A181945 1,3
%A A181945 _Martin Renner_, Apr 03 2012
%E A181945 a(7)-a(38) from _Lucas A. Brown_, Feb 05 2024