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A077237 Combined Diophantine Chebyshev sequences A054491 and A077234. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A318193 A048083 A127931 * A056879 A006746 A205875

Adjacent sequences:  A077234 A077235 A077236 * A077238 A077239 A077240

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)