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A041895
Denominators of continued fraction convergents to sqrt(469).
2
1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480, 74170470529, 75909259009, 150079729538, 225988988547, 2409969615008, 14685806678595, 149268036400958
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +32*x^14 -195*x^13 +1982*x^12 -2177*x^11 +4159*x^10 -6336*x^9 -4159*x^8 -2177*x^7 -1982*x^6 -195*x^5 -32*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -274430*x^10 +1). - Colin Barker, Nov 26 2013
a(n) = 274430*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[469], 30]] (* Vincenzo Librandi, Dec 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 274430, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480}, 30] (* Harvey P. Dale, Mar 23 2023 *)
PROG
(Magma) I:=[1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480]; [n le 20 select I[n] else 274430*Self(n-10)-Self(n-20): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 26 2013
STATUS
approved