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A042674
Numerators of continued fraction convergents to sqrt(867).
2
29, 59, 265, 7744, 31241, 70226, 4104349, 8278924, 37220045, 1087660229, 4387860961, 9863382151, 576464025719, 1162791433589, 5227629760075, 152764054475764, 616283847663131, 1385331749802026, 80965525336180639
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 140452, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (29 +59*x +265*x^2 +7744*x^3 +31241*x^4 +70226*x^5 +31241*x^6 -7744*x^7 +265*x^8 -59*x^9 +29*x^10 -x^11)/(1 -140452*x^6 +x^12). - Vincenzo Librandi, Dec 01 2013
a(n) = 140452*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 01 2013
MATHEMATICA
Numerator[Convergents[Sqrt[867], 30]] (* or *) CoefficientList[Series[(29 + 59 x + 265 x^2 + 7744 x^3 + 31241 x^4 + 70226 x^5 + 31241 x^6 - 7744 x^7 + 265 x^8 - 59 x^9 + 29 x^10 - x^11)/(1 - 140452 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 01 2013 *)
PROG
(Magma) I:=[29, 59, 265, 7744, 31241, 70226, 4104349, 8278924, 37220045, 1087660229, 4387860961, 9863382151]; [n le 12 select I[n] else 140452*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 01 2013
CROSSREFS
Cf. A042675.
Sequence in context: A196940 A104119 A356717 * A078948 A269263 A042676
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved