cp's OEIS Frontend

A181947 Number of rhombi, distinct up to congruence, on an n X n grid (or geoboard).

%I A181947 #20 Feb 16 2025 08:33:13
%S A181947 0,1,3,6,11,16,24,31,43,53,67,78,99,112,132,151,179,196,226,245,282,
%T A181947 309,341,364,416,445,483,517,570,599,659,690,754,797,847,894,975,1012,
%U A181947 1068,1119,1211,1252,1338,1381,1466,1536,1604,1651,1775,1833,1923,1990,2091
%N A181947 Number of rhombi, distinct up to congruence, on an n X n grid (or geoboard).
%H A181947 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A181947.py">Python program</a>.
%H A181947 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rhombus.html">Rhombus</a>.
%e A181947 a(1) = 0 because the 1 X 1 grid has no rhombi.
%e A181947 a(2) = 1 because the 2 X 2 grid has one rhombus.
%e A181947 a(3) = 3 because the 3 X 3 grid has 3 congruence classes of rhombi (all of which are squares) out of 6 rhombi total.
%e A181947 a(3) = 6 because the 4 X 4 grid has 6 congruence classes of rhombi, out of 22 rhombi total:
%e A181947 +---------+---------+---------+
%e A181947 | . . . . | . . . . | . . . . |
%e A181947 | . . . . | o . o . | . o . . |
%e A181947 | o o . . | . . . . | o . o . |
%e A181947 | o o . . | o . o . | . o . . |
%e A181947 +---------+---------+---------+
%e A181947 | o . . o | . . . o | . o . . |
%e A181947 | . . . . | . o . . | . . . o |
%e A181947 | . . . . | . . o . | o . . . |
%e A181947 | o . . o | o . . . | . . o . |
%e A181947 +---------+---------+---------+
%Y A181947 Cf. A181944, A189418.
%K A181947 nonn
%O A181947 1,3
%A A181947 _Martin Renner_, Apr 03 2012
%E A181947 a(7)-a(53) from _Lucas A. Brown_, Feb 08 2024