A077411 Combined Diophantine Chebyshev sequences A077409 and A077250.

7, 11, 59, 103, 583, 1019, 5771, 10087, 57127, 99851, 565499, 988423, 5597863, 9784379, 55413131, 96855367, 548533447, 958769291, 5429921339, 9490837543, 53750679943, 93949606139, 532076878091, 930005223847, 5267018100967

Offset: 0

Author

Wolfdieter Lang, Nov 08 2002

Keywords

• nonn
• easy

Comments

a(n)^2 - 24*b(n)^2 = 25, with the companion sequence b(n)= A077410(n).

Examples

			59 = a(2) = sqrt(24*A077410(2)^2 + 25) = sqrt(24*12^2 + 25)= sqrt(3481) = 59.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Chebyshev polynomials.
• Index entries for linear recurrences with constant coefficients, signature (0,10,0,-1).

Programs

Magma

I:=[7,11,59,103]; [n le 4 select I[n] else 10*Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 18 2018

Mathematica

CoefficientList[Series[(1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4), {x,0,50}], x] (* or *) LinearRecurrence[{0,10,0,-1}, {7,11,59,103}, 30] (* G. C. Greubel, Jan 18 2018 *)

PARI

x='x+O('x^30); Vec((1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4)) \\ G. C. Greubel, Jan 18 2018

Formula

a(2*k)= A077409(k) and a(2*k+1)= A077250(k), k>=0.

a(n)= sqrt(24*A077410(n)^2 + 25).

G.f.: (1-x)*(7+18*x+7*x^2)/(1-10*x^2+x^4).