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A077411 Combined Diophantine Chebyshev sequences A077409 and A077250. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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).

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).

EXAMPLE

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

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 *)

PROG

(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

(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

CROSSREFS

Sequence in context: A038277 A045462 A263231 * A085016 A067690 A196181

Adjacent sequences:  A077408 A077409 A077410 * A077412 A077413 A077414

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)