A076295 Consider all Pythagorean triples (Y-7,Y,Z); sequence gives Y values.

4, 7, 12, 15, 28, 55, 72, 147, 304, 403, 840, 1755, 2332, 4879, 10212, 13575, 28420, 59503, 79104, 165627, 346792, 461035, 965328, 2021235, 2687092, 5626327, 11780604, 15661503, 32792620, 68662375, 91281912, 191129379, 400193632, 532029955, 1113983640

Offset: 0

Author

Henry Bottomley, Oct 05 2002

Keywords

• nonn

Comments

First two terms included for consistency with A076293.

Examples

			15 is in the sequence as the longer leg of the (8,15,17) triangle.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).

Crossrefs

Cf. A046090, A076293, A076294, A076296.

Programs

Mathematica

LinearRecurrence[{1,0,6,-6,0,-1,1},{4,7,12,15,28,55,72},40] (* Harvey P. Dale, Feb 02 2012 *)

Formula

a(n) =6a(n-3)-a(n-6)-14 =(A076293(n)+7)/2 =sqrt(A076294(n)^2-A076296(n)^2) =A076296(n)+7.

a(3n+1) = 7*A046090(n).

a(0)=4, a(1)=7, a(2)=12, a(3)=15, a(4)=28, a(5)=55, a(6)=72, a(n)= a(n-1)+ 6*a(n-3)-6*a(n-4)-a(n-6)+a (n-7). - Harvey P. Dale, Feb 02 2012

G.f.: -(3*x^6-3*x^5-5*x^4-21*x^3+5*x^2+3*x+4) / ((x-1)*(x^6-6*x^3+1)). - Colin Barker, Sep 14 2014