A118554 - OEIS

%I #25 Sep 08 2022 08:45:25

%S 0,11,35,56,104,147,204,336,455,731,980,1311,2079,2772,4380,5831,7760,

%T 12236,16275,25647,34104,45347,71435,94976,149600,198891,264420,

%U 416472,553679,872051,1159340,1541271,2427495,3227196,5082804,6757247,8983304

%N a(n) = 6*a(n-5) - a(n-10) + 98 with a(0)=0, a(1)=11, a(2)=35, a(3)=56, a(4)=104, a(5)=147, a(6)=204, a(7)=336, a(8)=455, a(9)=731.

%C X values of solutions to the equation X^2 + (X+49)^2 = Y^2.

%C Consider all Pythagorean triples (X,X+49,Z) ordered by increasing Z; sequence gives X values.

%H G. C. Greubel, <a href="/A118554/b118554.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,6,-6,0,0,0,-1,1).

%F a(n) = a(n-1) +6*a(n-5) -6*a(n-6) -a(n-10) +a(n-11) with a(0)=0, a(1)=11, a(2)=35, a(3)=56, a(4)=104, a(5)=147, a(6)=204, a(7)=336, a(8)=455, a(9)=731, a(10)=980. - _Harvey P. Dale_, Aug 19 2011

%F G.f.: x*(11+24*x+21*x^2+48*x^3+43*x^4-9*x^5-12*x^6-7*x^7-12*x^8 -9*x^9)/( (1-x)*(1-6*x^5+x^10)). - _Colin Barker_, Apr 09 2012

%t LinearRecurrence[{1,0,0,0,6,-6,0,0,0,-1,1}, {0,11,35,56,104, 147,204,336, 455,731,980},40] (* _Harvey P. Dale_, Aug 19 2011 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(x*(11+24*x+21*x^2+48*x^3+43*x^4 -9*x^5-12*x^6-7*x^7-12*x^8 -9*x^9)/((1-x)*(1-6*x^5+x^10)))) \\ _G. C. Greubel_, May 07 2018

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(11+24*x+21*x^2+48*x^3+43*x^4-9*x^5-12*x^6 -7*x^7 -12*x^8 -9*x^9)/( (1-x)*(1-6*x^5+x^10)))); // _G. C. Greubel_, May 07 2018

%K nonn,easy

%O 0,2

%A _Mohamed Bouhamida_, May 07 2006