A077237 Combined Diophantine Chebyshev sequences A054491 and A077234.

1, 2, 6, 9, 23, 34, 86, 127, 321, 474, 1198, 1769, 4471, 6602, 16686, 24639, 62273, 91954, 232406, 343177, 867351, 1280754, 3236998, 4779839, 12080641, 17838602, 45085566, 66574569, 168261623

Offset

0,2

Comments

-3*a(n)^2 + b(n)^2 = 13, with the companion sequence b(n)= A077238(n).

Links

Matthew House, Table of n, a(n) for n = 0..3478

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)= A054491(k) and a(2*k+1)= A077234(k), k>=0.

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

a(n) = 4*a(n-2) - a(n-4). - Matthew House, Feb 11 2017

Example

3*a(2)^2 + 13 = 3*36+13 = 121 = 11^2 = A077238(2)^2.

Mathematica

CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - 4 x^2 + x^4), {x, 0, 28}], x] (* Michael De Vlieger, Feb 11 2017 *)

Crossrefs

Sequence in context: A048083 A127931 A346673 * A056879 A006746 A205875

Adjacent sequences: A077234 A077235 A077236 * A077238 A077239 A077240

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved