A067011 - OEIS

%I #13 Sep 22 2023 13:48:06

%S 33,32,683,781,15323,17470,343253,391369,7689473,8767348,172257683,

%T 196403977,3858874283,4399793626,86445553373,98563095565,

%U 1936532042753,2207986245064,43381714920923,49462765251493,971826516645083,1108052711738422,21770618800480133

%N a(2n) and a(2n+1) are side lengths of a Beentjes sequence of perfect squared rectangles, starting with a 33 X 32 rectangle.

%H Colin Barker, <a href="/A067011/b067011.txt">Table of n, a(n) for n = 0..1000</a>

%H P. Beentjes, <a href="http://www.nieuwarchief.nl/serie5/pdf/naw5-2000-01-3-344.pdf">An algorithm for the generation of perfect squared rectangles of arbitrary dimension</a>, Nieuw Arch. Wisk. 5/1 (2000) 344.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,22,0,9).

%F a(2n) = 11a(2n-2)+10a(2n-1), a(2n+1) = 13a(2n-2)+11a(2n-1), a(0) = 33, a(1) = 32.

%F a(n) = 22*a(n-2)+9*a(n-4) for n>3. - _Colin Barker_, May 28 2015

%F G.f.: -(77*x^3-43*x^2+32*x+33) / (9*x^4+22*x^2-1). - _Colin Barker_, May 28 2015

%t LinearRecurrence[{0,22,0,9},{33,32,683,781},30] (* _Harvey P. Dale_, Sep 22 2023 *)

%o (PARI) Vec(-(77*x^3-43*x^2+32*x+33) / (9*x^4+22*x^2-1) + O(x^100)) \\ _Colin Barker_, May 28 2015

%Y Cf. A067010.

%K easy,nonn

%O 0,1

%A _Floor van Lamoen_, Dec 26 2001