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A042370
Numerators of continued fraction convergents to sqrt(712).
2
26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401, 270075866, 275202267, 820480400, 5198084667, 11216649734, 16414734401, 864782838586, 881197572987, 2627177984560, 16644265480347
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3202,0,0,0,0,0,-1).
FORMULA
G.f.: (26 + 27*x + 80*x^2 + 507*x^3 + 1094*x^4 + 1601*x^5 + 1094*x^6 - 507*x^7 + 80*x^8 - 27*x^9 + 26*x^10 - x^11)/(1 - 3202*x^6 + x^12). - Vincenzo Librandi, Nov 22 2013
a(n) = 3202*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 22 2013
MATHEMATICA
Numerator[Convergents[Sqrt[712], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 80 x^2 + 507 x^3 + 1094 x^4 + 1601 x^5 + 1094 x^6 - 507 x^7 + 80 x^8 - 27 x^9 + 26 x^10 - x^11)/(1 - 3202 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 3202, 0, 0, 0, 0, 0, -1}, {26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401}, 40] (* Harvey P. Dale, Jul 08 2018 *)
PROG
(Magma) I:=[26, 27, 80, 507, 1094, 1601, 84346, 85947, 256240, 1623387, 3503014, 5126401]; [n le 12 select I[n] else 3202*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 22 2013
CROSSREFS
Cf. A042371.
Sequence in context: A042374 A042376 A042372 * A042382 A042380 A042378
KEYWORD
nonn,cofr,frac,easy
STATUS
approved