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A077410 Combined Diophantine Chebyshev sequences A077249 and A077251. 2
1, 2, 12, 21, 119, 208, 1178, 2059, 11661, 20382, 115432, 201761, 1142659, 1997228, 11311158, 19770519, 111968921, 195707962, 1108378052, 1937309101, 10971811599, 19177383048, 108609737938 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

-24*a(n)^2 + b(n)^2 = 25, with the companion sequence b(n)= A077411(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) = A077251(k) and a(2*k+1) = A077249(k), k>=0.

a(n) = sqrt((A077411(n)^2 - 25)/24).

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

EXAMPLE

24*a(2)^2 + 25 = 24*12^2 + 25 = 3481 = 59^2 = A077411(2)^2.

MATHEMATICA

CoefficientList[Series[(1+x)*(1+x+x^2)/(1-10*x^2+x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 10, 0, -1}, {1, 2, 12, 21}, 30] (* G. C. Greubel, Jan 18 2018 *)

PROG

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

(MAGMA) I:=[1, 2, 12, 21]; [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: A155890 A213969 A199986 * A211029 A225188 A193828

Adjacent sequences:  A077407 A077408 A077409 * A077411 A077412 A077413

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 08 2002

STATUS

approved

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Last modified November 11 15:51 EST 2019. Contains 329019 sequences. (Running on oeis4.)