A076295 - OEIS

%I #14 Jun 18 2017 02:25:43

%S 4,7,12,15,28,55,72,147,304,403,840,1755,2332,4879,10212,13575,28420,

%T 59503,79104,165627,346792,461035,965328,2021235,2687092,5626327,

%U 11780604,15661503,32792620,68662375,91281912,191129379,400193632,532029955,1113983640

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

%C First two terms included for consistency with A076293.

%H Harvey P. Dale, <a href="/A076295/b076295.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,6,-6,0,-1,1).

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

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

%F 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

%F 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

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

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

%Y Cf. A046090, A076293, A076294, A076296.

%K nonn

%O 0,1

%A _Henry Bottomley_, Oct 05 2002