A123006 Expansion of x^2/(1 -2*x -121*x^2).

0, 1, 2, 125, 492, 16109, 91750, 2132689, 15367128, 288789625, 2437001738, 39817548101, 374512306500, 5566947933221, 56449884952942, 786500469825625, 8403437018957232, 111973430886815089, 1240762741067455250

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 23 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..800
• Index entries for linear recurrences with constant coefficients, signature (2, 121).

Crossrefs

Sequences of the form (m*i)^(n-1)*ChebyshevU(n-1, -i/m): A131577 (m=0), A000129 (m=1), A085449 (m=2), A002534 (m=3), A161007 (m=4), A123004 (m=5), A123005 (m=7), this sequence (m=11).

Programs

Magma

[n le 2 select n-1 else 2*Self(n-1) + 121*Self(n-2): n in [1..30]]; // G. C. Greubel, Jul 12 2021

Mathematica

Rest@CoefficientList[Series[x^2/(1 -2*x -121*x^2), {x,0,30}], x]

Sage

[(11*i)^(n-2)*chebyshev_U(n-2, -i/11) for n in [1..30]] # G. C. Greubel, Jul 12 2021

Formula

a(n) = 2*a(n-1) + 121*a(n-2).

a(n) = (11*i)^(n-2)*ChebyshevU(n-2, -i/11). - G. C. Greubel, Jul 12 2021