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A042896
Numerators of continued fraction convergents to sqrt(980).
2
31, 94, 313, 407, 720, 1847, 2567, 4414, 15809, 51841, 3229951, 9741694, 32455033, 42196727, 74651760, 191500247, 266152007, 457652254, 1639108769, 5374978561, 334887779551, 1010038317214, 3365002731193, 4375041048407, 7740043779600, 19855128607607, 27595172387207, 47450300994814, 169946075371649
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 103682, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (31 + 94*x + 313*x^2 + 407*x^3 + 720*x^4 + 1847*x^5 + 2567*x^6 + 4414*x^7 + 15809*x^8 + 51841*x^9 + 15809*x^10 - 4414*x^11 + 2567*x^12 - 1847*x^13 + 720*x^14 - 407*x^15 + 313*x^16 - 94*x^17 + 31*x^18 - x^19) / (1 - 103682*x^10 + x^20). - Vincenzo Librandi, Dec 08 2013
a(n) = 103682*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 08 2013
MATHEMATICA
Numerator[Convergents[Sqrt[980], 30]] (* or *) CoefficientList[Series[(31 + 94 x + 313 x^2 + 407 x^3 + 720 x^4 + 1847 x^5 + 2567 x^6+4414 x^7 + 15809 x^8 + 51841 x^9 + 15809 x^10 - 4414 x^11 + 2567 x^12 - 1847 x^13 + 720 x^14 - 407 x^15 + 313 x^16 - 94 x^17 + 31 x^18 - x^19) / (1 - 103682 x^10 + x^20), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 08 2013 *)
PROG
(Magma) I:=[31, 94, 313, 407, 720, 1847, 2567, 4414, 15809, 51841, 3229951, 9741694, 32455033, 42196727, 74651760, 191500247, 266152007, 457652254, 1639108769, 5374978561]; [n le 20 select I[n] else 103682*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Dec 08 2013
CROSSREFS
Cf. A042897.
Sequence in context: A042892 A042890 A042894 * A042898 A044218 A044599
KEYWORD
nonn,cofr,frac,easy
EXTENSIONS
More terms from Vincenzo Librandi, Dec 08 2013
STATUS
approved