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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 (list; graph; refs; listen; history; text; internal format)
 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 Vincenzo Librandi, Table of n, a(n) for n = 0..200 R. Alter, On the non-existence of perfect double Hamming-error-correcting codes on q=8 and q=9 symbols, Information and Control 13 (6) (1968) 619-627. 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 Cf. A041298, A010211. Sequence in context: A079940 A225205 A041299 * A042079 A045826 A084200 Adjacent sequences:  A001109 A001110 A001111 * A001113 A001114 A001115 KEYWORD nonn,frac,easy AUTHOR EXTENSIONS Edited by R. J. Mathar, Aug 31 2009 More terms from Colin Barker, Nov 23 2013 STATUS approved

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Last modified October 27 17:25 EDT 2020. Contains 338035 sequences. (Running on oeis4.)