A041895 Denominators of continued fraction convergents to sqrt(469).
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- 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).
Programs
-
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
-
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 *)
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
Extensions
More terms from Colin Barker, Nov 26 2013