A118554 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.

0, 11, 35, 56, 104, 147, 204, 336, 455, 731, 980, 1311, 2079, 2772, 4380, 5831, 7760, 12236, 16275, 25647, 34104, 45347, 71435, 94976, 149600, 198891, 264420, 416472, 553679, 872051, 1159340, 1541271, 2427495, 3227196, 5082804, 6757247, 8983304

Offset: 0

Author

Mohamed Bouhamida, May 07 2006

Keywords

• nonn
• easy

Comments

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

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

Links

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

Programs

Magma

m:=25; R:=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

Mathematica

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 *)

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

Formula

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

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