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A041907
Denominators of continued fraction convergents to sqrt(475).
2
1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896, 13119332617, 13425898513, 53397028156, 66822926669, 454334588170, 975492103009, 6307287206224, 7282779309233
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 115598, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -x^17 +4*x^16 -5*x^15 +34*x^14 -73*x^13 +472*x^12 -545*x^11 +2107*x^10 -2652*x^9 -2107*x^8 -545*x^7 -472*x^6 -73*x^5 -34*x^4 -5*x^3 -4*x^2 -x -1) / ((x^10 -340*x^5 +1)*(x^10 +340*x^5 +1)). - Colin Barker, Nov 27 2013
a(n) = 115598*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 27 2013
MATHEMATICA
Denominator[Convergents[Sqrt[475], 30]] (* Vincenzo Librandi, Dec 27 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 115598, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896}, 30] (* Harvey P. Dale, Jul 08 2020 *)
PROG
(Magma) I:=[1, 1, 4, 5, 34, 73, 472, 545, 2107, 2652, 113491, 116143, 461920, 578063, 3930298, 8438659, 54562252, 63000911, 243564985, 306565896]; [n le 20 select I[n] else 115598*Self(n-10)-Self(n-20): n in [1..50]]; // Vincenzo Librandi, Dec 27 2013
CROSSREFS
Sequence in context: A013468 A376536 A244333 * A228662 A151450 A243772
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 27 2013
STATUS
approved