A120892 a(n)=3*a(n-1)+3*a(n-2)-a(n-3);a(0)=1,a(1)=0,a(2)=3. a(n)=4*{a(n-1)+(-1)^n}-a(n-2);a(0)=1,a(1)=0.

1, 0, 3, 8, 33, 120, 451, 1680, 6273, 23408, 87363, 326040, 1216801, 4541160, 16947843, 63250208, 236052993, 880961760, 3287794051, 12270214440, 45793063713, 170902040408, 637815097923, 2380358351280, 8883618307201

Offset

0,3

Comments

For n>1, short leg of primitive Pythagorean triangles having an angle nearing pi/3 with larger values of sides.[Complete triple (X,Y,Z),X<Y<Z is given by X=a(n),Y=A001353(n),Z=A120893(n), with recurrence relations Y(i+1)=2*{Y(i)-(-1)^i} + 3*a(i) ; Z(i+1)=2*{2*Z(i)-a(i-1)} - 3*(-1)^i] A120893(n)=2*a(n)-(-1)^n.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

J. P. Chabert, Right Triangle Applet (Hypotenuse & angles computation, given legs<350)

Index entries for linear recurrences with constant coefficients, signature (3, 3, -1).

Formula

Union of A045899 and A011922.

O.g.f.: -(-1+3*x)/((x+1)*(x^2-4*x+1)). - R. J. Mathar, Nov 23 2007

Mathematica

LinearRecurrence[{3, 3, -1}, {1, 0, 3}, 30] (* Harvey P. Dale, Mar 05 2014 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 3, 3]^n*[1; 0; 3])[1, 1] \\ Charles R Greathouse IV, Oct 19 2022

Crossrefs

Sequence in context: A284963 A148916 A148917 * A195499 A225688 A109655

Adjacent sequences: A120889 A120890 A120891 * A120893 A120894 A120895

Keyword

nonn,easy

Author

Lekraj Beedassy, Jul 13 2006

Extensions

Corrected and extended by T. D. Noe, Nov 07 2006

Status

approved