A040879 -id:A040879 - cp's OEIS frontend

A042759 Denominators of continued fraction convergents to sqrt(910).

1, 6, 361, 2172, 130681, 786258, 47306161, 284623224, 17124699601, 103032820830, 6199093949401, 37297596517236, 2244054884983561, 13501626906418602, 812341669270099681, 4887551642527016688, 294065440220891100961, 1769280192967873622454

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,362,0,-1).

Cf. A042758, A040879.

Denominator[Convergents[Sqrt[910], 30]] (* Vincenzo Librandi, Jan 28 2014 *)
LinearRecurrence[{0,362,0,-1},{1,6,361,2172},20] (* Harvey P. Dale, Dec 10 2017 *)

G.f.: -(x^2-6*x-1) / (x^4-362*x^2+1). - Colin Barker, Dec 23 2013

More terms from Colin Barker, Dec 23 2013

A228838 a(n) = n * A002445(n).

Original entry on oeis.org

0, 6, 60, 126, 120, 330, 16380, 42, 4080, 7182, 3300, 1518, 32760, 78, 12180, 214830, 8160, 102, 34545420, 114, 270600, 37926, 15180, 6486, 1113840, 1650, 41340, 21546, 24360, 10266, 1703601900, 186, 16320, 2135826, 1020, 164010, 5043631320, 222, 1140

Offset: 0

Paul Curtz, Sep 05 2013

nonn

a(n+1) is a multiple of A040031(n+1), sequence of period 2: 6, 12.
a(n) is divisible by A040879(n)=30 followed by the sequence of period 2: 6, 60. See A040214 and A165734.
Note that A164877(n) + A000367(n) = A164558(2n).

			a(0)=0*1, a(1)=1*6, a(2)=2*30=60,, a(3)=3*42=126.

Colin Barker, Table of n, a(n) for n = 0..1000

PARI
```
a(n)=n*denominator(bernfrac(2*n))
```

a(n) = A176328(2n) - A000367(n).
a(n) = A164877(n)/2.
a(n+1) = A111008(n) * A036283(n+1).
2*a(n) = A164558(2n) - A000367(n).
a(n) = A164558(2n) - A176328(2n).

Typo in data fixed by Colin Barker, Jul 03 2015

cp's OEIS Frontend

A042759 Denominators of continued fraction convergents to sqrt(910).

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