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A211415 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + x*y = 1.

%I A211415 #23 Sep 08 2022 08:46:02
%S A211415 0,12,20,36,52,68,84,100,132,148,164,180,212,228,244,276,308,324,340,
%T A211415 356,388,420,436,452,516,532,548,564,596,612,644,660,692,724,740,772,
%U A211415 804,820,836,868,932,948,980,996,1028,1060,1076,1092,1156,1172
%N A211415 Number of ordered triples (w,x,y) with all terms in  {-n,...,0,...,n} and w^2 + x*y = 1.
%C A211415 For n>0, a(n)+2 is the number of self-inverse 2 X 2 matrices with all terms in {-n,...,0,...,n} (see A211416).
%C A211415 For a guide to related sequences, see A211422.
%H A211415 Chai Wah Wu, <a href="/A211415/b211415.txt">Table of n, a(n) for n = 0..10000</a>
%F A211415 For n>0, a(n+1) - a(n) = 8*A060594(n+1). - _Pontus von Brömssen_, Jan 22 2020
%t A211415 t[n_] := t[n] = Flatten[Table[w^2 + x*y - 1, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
%t A211415 c[n_] := Count[t[n], 0]
%t A211415 t = Table[c[n], {n, 0, 20}]  (* A211415 *)
%t A211415 t + 2                        (* A211416 *)
%t A211415 (t + 2)/2    (* integers *)
%t A211415 t/4          (* integers *)
%t A211415 (t/4 - 1)/4  (* integers for n>1 *)
%o A211415 (Magma) a:=[]; for n in [0..50] do Append(~a,#[<w,x,y>:w,x,y in [-n..n]|w^2 + x*y eq 1]); end for; a; // _Marius A. Burtea_, Jan 22 2020
%Y A211415 Cf. A060594, A211416, A211422.
%K A211415 nonn
%O A211415 0,2
%A A211415 _Clark Kimberling_, Apr 09 2012