A067011 a(2n) and a(2n+1) are side lengths of a Beentjes sequence of perfect squared rectangles, starting with a 33 X 32 rectangle.

33, 32, 683, 781, 15323, 17470, 343253, 391369, 7689473, 8767348, 172257683, 196403977, 3858874283, 4399793626, 86445553373, 98563095565, 1936532042753, 2207986245064, 43381714920923, 49462765251493, 971826516645083, 1108052711738422, 21770618800480133

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

P. Beentjes, An algorithm for the generation of perfect squared rectangles of arbitrary dimension, Nieuw Arch. Wisk. 5/1 (2000) 344.

Index entries for linear recurrences with constant coefficients, signature (0,22,0,9).

Formula

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

a(n) = 22*a(n-2)+9*a(n-4) for n>3. - Colin Barker, May 28 2015

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

Mathematica

LinearRecurrence[{0, 22, 0, 9}, {33, 32, 683, 781}, 30] (* Harvey P. Dale, Sep 22 2023 *)

Prog

(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

Crossrefs

Cf. A067010.

Sequence in context: A304261 A022989 A023475 * A291436 A165854 A112817

Adjacent sequences: A067008 A067009 A067010 * A067012 A067013 A067014

Keyword

easy,nonn

Author

Floor van Lamoen, Dec 26 2001

Status

approved