A156866 - OEIS

A156866

a(n) = 729000*n - 116820.

612180, 1341180, 2070180, 2799180, 3528180, 4257180, 4986180, 5715180, 6444180, 7173180, 7902180, 8631180, 9360180, 10089180, 10818180, 11547180, 12276180, 13005180, 13734180, 14463180, 15192180, 15921180, 16650180, 17379180

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OFFSET

1,1

COMMENTS

The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as A157079(n)^2 - A156854(n)*a(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

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

G.f.: 180*x*(3401+649*x)/(1-x)^2.

E.g.f.: 180*(649 - (649 - 4050*x)*exp(x)). - G. C. Greubel, Jan 28 2022

MATHEMATICA

LinearRecurrence[{2, -1}, {612180, 1341180}, 40]

PROG

(Magma) I:=[612180, 1341180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

(PARI) a(n)=729000*n-116820 \\ Charles R Greathouse IV, Dec 23 2011