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A041006 Numerators of continued fraction convergents to sqrt(6). 15
2, 5, 22, 49, 218, 485, 2158, 4801, 21362, 47525, 211462, 470449, 2093258, 4656965, 20721118, 46099201, 205117922, 456335045, 2030458102, 4517251249, 20099463098, 44716177445, 198964172878, 442644523201, 1969542265682, 4381729054565, 19496458483942 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Interspersion of 2 sequences, 2*A054320 and A001079. - Gerry Martens, Jun 10 2015
LINKS
FORMULA
From M. F. Hasler, Feb 13 2009: (Start)
a(2n) = 2*A142238(2n) = A041038(2n)/2;
a(2n-1) = A142238(2n-1) = A041038(2n-1) = A001079(n). (End)
G.f.: (2 + 5*x + 2*x^2 - x^3)/(1 - 10*x^2 + x^4).
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[6], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)
LinearRecurrence[{0, 10, 0, -1}, {2, 5, 22, 49}, 50] (* Vincenzo Librandi, Jun 10 2015 *)
PROG
(Magma) I:=[2, 5, 22, 49]; [n le 4 select I[n] else 10*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 10 2015
From M. F. Hasler, Nov 01 2019: (Start)
(PARI) A41006=contfracpnqn(c=contfrac(sqrt(6)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A41006[n+1]! For correct index & more terms:
A041006(n)={n<#A041006|| A041006=extend(A041006, [2, 10; 4, -1], n\.8); A041006[n+1]}
extend(A, c, N)={for(n=#A+1, #A=Vec(A, N), A[n]=[A[n-i]|i<-c[, 1]]*c[, 2]); A} \\ (End)
CROSSREFS
Cf. A041007 (denominators).
Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).
Sequence in context: A357020 A181443 A041165 * A346557 A288028 A083465
KEYWORD
nonn,cofr,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Jun 10 2015
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)