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A041018
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Numerators of continued fraction convergents to sqrt(13).
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14
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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
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OFFSET
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0,1
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LINKS
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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).
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn,frac,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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