cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A175383 Number of complete quadrangles on an n X n grid (or geoplane).

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%I A175383 #36 Feb 16 2025 08:33:12
%S A175383 0,1,78,1278,9498,47331,175952,545764,1461672,3507553,7701638,
%T A175383 15773526,30375194,55695587,97777392,165310348,270478344,430196181,
%U A175383 666685134,1010083690,1498720098,2182544223
%N A175383 Number of complete quadrangles on an n X n grid (or geoplane).
%C A175383 A complete quadrangle is a set of four points, no three collinear, and the six lines which join them.
%C A175383 Number of ways to arrange 4 indistinguishable points on an n X n square grid so that no three points are collinear at any angle. Column 4 of A194193. - _R. H. Hardin_, Aug 18 2011
%H A175383 R. H. Hardin, <a href="/A175383/b175383.txt">Table of n, a(n) for n = 1..55</a>
%H A175383 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteQuadrangle.html">Complete Quadrangle</a>.
%F A175383 a(n) = A189345(n) - A189346(n) - A178256(n).
%F A175383 a(n) = (1/3)*A189412(n) + A189413(n).
%e A175383 From _R. H. Hardin_, Aug 18 2011: (Start)
%e A175383 Some solutions for 3 X 3:
%e A175383   0 1 1   1 1 0   1 0 1   0 1 1   0 0 0   1 1 0   1 1 0
%e A175383   1 0 0   0 0 0   1 0 0   1 1 0   1 1 0   0 0 1   1 0 0
%e A175383   1 0 0   1 0 1   0 0 1   0 0 0   0 1 1   0 1 0   0 1 0
%e A175383 (End)
%K A175383 nonn
%O A175383 1,3
%A A175383 _Martin Renner_, Apr 19 2011
%E A175383 a(6)-a(22) from _Nathaniel Johnston_, Apr 25 2011
%E A175383 a(7)-a(22) corrected by _Nathaniel Johnston_, based on another correction by Michal ForiĊĦek, Sep 06 2011