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 A041018 Numerators of continued fraction convergents to sqrt(13). 14
 3, 4, 7, 11, 18, 119, 137, 256, 393, 649, 4287, 4936, 9223, 14159, 23382, 154451, 177833, 332284, 510117, 842401, 5564523, 6406924, 11971447, 18378371, 30349818, 200477279, 230827097, 431304376, 662131473 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,36,0,0,0,0,1). FORMULA From Johannes W. Meijer, Jun 12 2010: (Start) a(5*n) = A006497(3*n+1), a(5*n+1) = (A006497(3*n+2)-A006497(3*n+1))/2, a(5*n+2) = (A006497(3*n+2)+A006497(3*n+1))/2, a(5*n+3) = A006497(3*n+2), a(5*n+4) = A006497(3*n+3)/2. (End) G.f.: (3 + 4*x + 7*x^2 + 11*x^3 + 18*x^4 + 11*x^5 - 7*x^6 + 4*x^7 - 3*x^8 + x^9)/(1 - 36*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013 a(n) = A010122(n)*a(n-1)+a(n-2) with a(0)=3, a(-1)=1. - Paul Weisenhorn, Aug 19 2018 MAPLE a[0]:=3: a[-1]:=1: b(0):=6: b(1):=1; b(2):=1: b(3):=1: b(4):=1: for n from 1 to 100 do  k:=n mod 5:    a[n]:=b(k)*a[n-1]+a[n-2]:    printf("%12d", a[n]): end do: # Paul Weisenhorn, Aug 17 2018 MATHEMATICA Numerator[Convergents[Sqrt[13], 30]] (* Vincenzo Librandi, Oct 27 2013 *) CoefficientList[Series[(3 + 4*x + 7*x^2 + 11*x^3 + 18*x^4 + 11*x^5 - 7*x^6 + 4*x^7 - 3*x^8 + x^9)/(1 - 36*x^5 - x^10), {x, 0, 50}], x] (* Stefano Spezia, Aug 31 2018 *) CROSSREFS Cf. A010122 (continued fraction for sqrt(13)). Cf. A010470, A041019 (denominators), A041046, A041090, A041150, A041226, A041318, A041426 and A041550. Sequence in context: A293420 A041739 A042593 * A072255 A049863 A025068 Adjacent sequences:  A041015 A041016 A041017 * A041019 A041020 A041021 KEYWORD nonn,frac,easy AUTHOR STATUS approved

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Last modified April 18 04:49 EDT 2021. Contains 343072 sequences. (Running on oeis4.)