A211416 - OEIS

%I #9 Jan 22 2020 09:58:49

%S 0,14,22,38,54,70,86,102,134,150,166,182,214,230,246,278,310,326,342,

%T 358,390,422,438,454,518,534,550,566,598,614,646,662,694,726,742,774,

%U 806,822,838,870,934,950,982,998,1030,1062,1078,1094,1158,1174

%N Number of self-inverse 2 X 2 matrices with all terms in {-n,...,0,...,n}.

%e The 14 matrices counted by a(1) are as follows:

%e   ...

%e 1 0...-1 0...-1 -1...-1 0...-1 0...-1 0...-1 1

%e 0 1... 0 -1...0  1...-1 1....0 1 ...1 1... 0 1

%e   ...

%e 0 -1...0 1...1 -1... 1 0....1 0....1 0....1 1

%e -1 0...1 0...0 -1...-1 -1...0 -1...1 -1...0 1

%t t[n_] := t[n] = Flatten[Table[w^2 + x*y - 1, {w, -n, n}, {x, -n, n}, {y, -n, n}]]

%t c[n_] := Count[t[n], 0]

%t t = Table[c[n], {n, 0, 20}]  (* A211415 *)

%t t + 2                        (* A211416 *)

%t (t + 2)/2    (* integers *)

%t t/4          (* integers *)

%t (t/4 - 1)/4  (* integers for n>1 *)

%Y Cf. A211415.

%K nonn

%O 0,2

%A _Clark Kimberling_, Apr 09 2012

%E Offset corrected by _Pontus von Brömssen_, Jan 22 2020