A001112 A continued fraction. (Formerly M2370 N0939)

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

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: A225205 A343931 A041299 * A042079 A045826 A346471

Adjacent sequences: A001109 A001110 A001111 * A001113 A001114 A001115

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Edited by R. J. Mathar, Aug 31 2009

More terms from Colin Barker, Nov 23 2013

Status

approved