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A001112
A continued fraction.
(Formerly M2370 N0939)
3
0, 1, 1, 3, 4, 11, 136, 283, 419, 1121, 1540, 38081, 39621, 117323, 156944, 431211, 5331476, 11094163, 16425639, 43945441, 60371080, 1492851361, 1553222441, 4599296243, 6152518684, 16904333611, 209004522016, 434913377643, 643917899659
OFFSET
0,4
COMMENTS
Ignoring a(0)=0 gives the denominators of continued fraction convergents to sqrt(162).
REFERENCES
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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,0,0,-1).
FORMULA
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
MATHEMATICA
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 *)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A225205 A343931 A041299 * A042079 A045826 A346471
KEYWORD
nonn,frac,easy
EXTENSIONS
Edited by R. J. Mathar, Aug 31 2009
More terms from Colin Barker, Nov 23 2013
STATUS
approved