login
A continued fraction.
(Formerly M2370 N0939)
3

%I M2370 N0939 #30 Sep 08 2022 08:44:28

%S 0,1,1,3,4,11,136,283,419,1121,1540,38081,39621,117323,156944,431211,

%T 5331476,11094163,16425639,43945441,60371080,1492851361,1553222441,

%U 4599296243,6152518684,16904333611,209004522016,434913377643,643917899659

%N A continued fraction.

%C Ignoring a(0)=0 gives the denominators of continued fraction convergents to sqrt(162).

%D R. Alter, On the non-existence of perfect double Hamming-error-correcting codes on q=8 and q=9 symbols. Information and Control 13 1968 619-627.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A001112/b001112.txt">Table of n, a(n) for n = 0..200</a>

%H R. Alter, <a href="http://dx.doi.org/10.1016/S0019-9958(68)91038-3">On the non-existence of perfect double Hamming-error-correcting codes on q=8 and q=9 symbols</a>, Information and Control 13 (6) (1968) 619-627.

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -x*(x^18 -x^17 +3*x^16 -4*x^15 +11*x^14 -136*x^13 +283*x^12 -419*x^11 +1121*x^10 -1540*x^9 -1121*x^8 -419*x^7 -283*x^6 -136*x^5 -11*x^4 -4*x^3 -3*x^2 -x -1) / ((x^10 -198*x^5 +1)*(x^10 +198*x^5 +1)). - _Colin Barker_, Nov 23 2013

%t CoefficientList[Series[-x (x^18 - x^17 + 3 x^16 - 4 x^15 + 11 x^14 - 136 x^13 + 283 x^12 - 419 x^11 + 1121 x^10 - 1540 x^9 - 1121 x^8 - 419 x^7 - 283 x^6 - 136 x^5 - 11 x^4 - 4 x^3 - 3 x^2 - x - 1)/((x^10 - 198 x^5 + 1) (x^10 + 198 x^5 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 14 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,0,0,-1},{0,1,1,3,4,11,136,283,419,1121,1540,38081,39621,117323,156944,431211,5331476,11094163,16425639,43945441},40] (* _Harvey P. Dale_, Jan 21 2015 *)

%o (Magma) I:=[0, 1, 1, 3, 4, 11, 136, 283, 419, 1121, 1540, 38081, 39621, 117323, 156944, 431211, 5331476, 11094163, 16425639, 43945441, 60371080]; [n le 21 select I[n] else 39202*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013

%Y Cf. A041298, A010211.

%K nonn,frac,easy

%O 0,4

%A _N. J. A. Sloane_

%E Edited by _R. J. Mathar_, Aug 31 2009

%E More terms from _Colin Barker_, Nov 23 2013