A041519 Denominators of continued fraction convergents to sqrt(276).

1, 1, 2, 3, 5, 13, 31, 75, 106, 181, 287, 468, 15263, 15731, 30994, 46725, 77719, 202163, 482045, 1166253, 1648298, 2814551, 4462849, 7277400, 237339649, 244617049, 481956698, 726573747, 1208530445, 3143634637, 7495799719, 18135234075, 25631033794

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,15550,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^22 -x^21 +2*x^20 -3*x^19 +5*x^18 -13*x^17 +31*x^16 -75*x^15 +106*x^14 -181*x^13 +287*x^12 -468*x^11 -287*x^10 -181*x^9 -106*x^8 -75*x^7 -31*x^6 -13*x^5 -5*x^4 -3*x^3 -2*x^2 -x -1) / ((x^8 -25*x^4 +1)*(x^16 +25*x^12 +624*x^8 +25*x^4 +1)). - Colin Barker, Nov 18 2013

a(n) = 15550*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[276], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 13, 31, 75, 106, 181, 287, 468, 15263, 15731, 30994, 46725, 77719, 202163, 482045, 1166253, 1648298, 2814551, 4462849, 7277400]; [n le 24 select I[n] else 15550*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041518, A040259.

Sequence in context: A162390 A108515 A167495 * A355512 A060434 A072999

Adjacent sequences: A041516 A041517 A041518 * A041520 A041521 A041522

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved