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A077238 Combined Diophantine Chebyshev sequences A077236 and A077235. 6
4, 5, 11, 16, 40, 59, 149, 220, 556, 821, 2075, 3064, 7744, 11435, 28901, 42676, 107860, 159269, 402539, 594400, 1502296, 2218331, 5606645, 8278924, 20924284, 30897365, 78090491, 115310536, 291437680, 430344779, 1087660229, 1606068580, 4059203236, 5993929541 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n)^2 - 3*b(n)^2 = 13, with the companion sequence b(n)= A077237(n).

Positive values of x (or y) satisfying x^2 - 4xy + y^2 + 39 = 0. - Colin Barker, Feb 06 2014

Positive values of x (or y) satisfying x^2 - 14xy + y^2 + 624 = 0. - Colin Barker, Feb 16 2014

LINKS

Vincenzo Librandi, 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 (0,4,0,-1).

FORMULA

a(2*k)= A077236(k) and a(2*k+1)= A077235(k), k>=0.

G.f.: (1-x)*(4+9*x+4*x^2)/(1-4*x^2+x^4).

a(n) = 4*a(n-2)-a(n-4). - Colin Barker, Feb 06 2014

EXAMPLE

11 = a(2) = sqrt(3*A077237(2)^2 + 13) = sqrt(3*6^2 + 13)= sqrt(121) = 11.

MATHEMATICA

CoefficientList[Series[(1 - x) (4 + 9 x + 4 x^2)/(1 - 4 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 07 2014 *)

LinearRecurrence[{0, 4, 0, -1}, {4, 5, 11, 16}, 40] (* Harvey P. Dale, Oct 23 2015 *)

CROSSREFS

Sequence in context: A066898 A118143 A001350 * A185507 A000286 A227620

Adjacent sequences:  A077235 A077236 A077237 * A077239 A077240 A077241

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

EXTENSIONS

More terms from Colin Barker, Feb 06 2014

STATUS

approved

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Last modified November 16 22:20 EST 2019. Contains 329208 sequences. (Running on oeis4.)