A211415 - OEIS

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

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OFFSET

0,2

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

FORMULA

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

PROG

(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

CROSSREFS

Cf. A060594, A211416, A211422.

Sequence in context: A082296 A187766 A260905 * A209973 A282754 A063690

Adjacent sequences: A211412 A211413 A211414 * A211416 A211417 A211418

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 09 2012

STATUS

approved