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A211416
Number of self-inverse 2 X 2 matrices with all terms in {-n,...,0,...,n}.
2
0, 14, 22, 38, 54, 70, 86, 102, 134, 150, 166, 182, 214, 230, 246, 278, 310, 326, 342, 358, 390, 422, 438, 454, 518, 534, 550, 566, 598, 614, 646, 662, 694, 726, 742, 774, 806, 822, 838, 870, 934, 950, 982, 998, 1030, 1062, 1078, 1094, 1158, 1174
OFFSET
0,2
EXAMPLE
The 14 matrices counted by a(1) are as follows:
...
1 0...-1 0...-1 -1...-1 0...-1 0...-1 0...-1 1
0 1... 0 -1...0 1...-1 1....0 1 ...1 1... 0 1
...
0 -1...0 1...1 -1... 1 0....1 0....1 0....1 1
-1 0...1 0...0 -1...-1 -1...0 -1...1 -1...0 1
MATHEMATICA
t[n_] := t[n] = Flatten[Table[w^2 + x*y - 1, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 20}] (* A211415 *)
t + 2 (* A211416 *)
(t + 2)/2 (* integers *)
t/4 (* integers *)
(t/4 - 1)/4 (* integers for n>1 *)
CROSSREFS
Cf. A211415.
Sequence in context: A183185 A324526 A259750 * A045282 A039291 A043114
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 09 2012
EXTENSIONS
Offset corrected by Pontus von Brömssen, Jan 22 2020
STATUS
approved