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, 0, 0, 613834, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: -(x^26 -x^25 +3*x^24 -4*x^23 +7*x^22 -11*x^21 +51*x^20 -266*x^19 +1115*x^18 -1381*x^17 +2496*x^16 -3877*x^15 +10250*x^14 -14127*x^13 -10250*x^12 -3877*x^11 -2496*x^10 -1381*x^9 -1115*x^8 -266*x^7 -51*x^6 -11*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/(x^28 -613834*x^14 +1). - Vincenzo Librandi, Dec 26 2013
a(n) = 613834*a(n-14) - a(n-28) for n>27. - Vincenzo Librandi, Dec 26 2013
MATHEMATICA
Denominator[Convergents[Sqrt[472], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 4 x^23 + 7 x^22 - 11 x^21 + 51 x^20 - 266 x^19 + 1115 x^18 - 1381 x^17 + 2496 x^16 - 3877 x^15 + 10250 x^14 - 14127 x^13 - 10250 x^12 - 3877 x^11 - 2496 x^10 - 1381 x^9 - 1115 x^8 - 266 x^7 - 51 x^6 - 11 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^28 - 613834 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 26 2013 *)
PROG
(Magma) I:=[1, 1, 3, 4, 7, 11, 51, 266, 1115, 1381, 2496, 3877, 10250, 14127, 603584, 617711, 1839006, 2456717, 4295723, 6752440, 31305483, 163279855, 684424903, 847704758, 1532129661, 2379834419, 6291798499, 8671632918]; [n le 28 select I[n] else 613834*Self(n-14)-Self(n-28): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 26 2013
STATUS
approved