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

0, 12, 20, 36, 52, 68, 84, 100, 132, 148, 164, 180, 212, 228, 244, 276, 308, 324, 340, 356, 388, 420, 436, 452, 516, 532, 548, 564, 596, 612, 644, 660, 692, 724, 740, 772, 804, 820, 836, 868, 932, 948, 980, 996, 1028, 1060, 1076, 1092, 1156, 1172

Offset: 0

Author

Clark Kimberling, Apr 09 2012

Keywords

• nonn

Comments

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).

For a guide to related sequences, see A211422.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A060594, A211416, A211422.

Programs

Magma

a:=[]; for n in [0..50] do Append(~a,#[:w,x,y in [-n..n]|w^2 + x*y eq 1]); end for; a; // Marius A. Burtea, Jan 22 2020

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 *)

Formula

For n>0, a(n+1) - a(n) = 8*A060594(n+1). - Pontus von Brömssen, Jan 22 2020