A077410 Combined Diophantine Chebyshev sequences A077249 and A077251.

1, 2, 12, 21, 119, 208, 1178, 2059, 11661, 20382, 115432, 201761, 1142659, 1997228, 11311158, 19770519, 111968921, 195707962, 1108378052, 1937309101, 10971811599, 19177383048, 108609737938

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: A213969 A199986 A336528 * A211029 A225188 A193828

Adjacent sequences: A077407 A077408 A077409 * A077411 A077412 A077413

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 08 2002

Status

approved