OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,170584,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^22 -x^21 +3*x^20 -4*x^19 +7*x^18 -67*x^17 +74*x^16 -733*x^15 +807*x^14 -1540*x^13 +3887*x^12 -5427*x^11 -3887*x^10 -1540*x^9 -807*x^8 -733*x^7 -74*x^6 -67*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/(x^24 -170584*x^12 +1). - Vincenzo Librandi, Dec 18 2013
a(n) = 170584*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 18 2013
MATHEMATICA
Denominator[Convergents[Sqrt[247], 30]] (* or *) CoefficientList[Series[-(x^22 - x^21 + 3 x^20 - 4 x^19 + 7 x^18 - 67 x^17 + 74 x^16 - 733 x^15 + 807 x^14 - 1540 x^13 + 3887 x^12 - 5427 x^11 - 3887 x^10 - 1540 x^9 - 807 x^8 - 733 x^7 - 74 x^6 - 67 x^5 - 7 x^4 - 4 x^3 - 3 x^2 - x - 1)/(x^24 - 170584 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 4, 7, 67, 74, 733, 807, 1540, 3887, 5427, 166697, 172124, 510945, 683069, 1194014, 11429195, 12623209, 125038076, 137661285, 262699361, 663060007, 925759368}, 30] (* Harvey P. Dale, Nov 29 2022 *)
PROG
(Magma) I:=[1, 1, 3, 4, 7, 67, 74, 733, 807, 1540, 3887, 5427, 166697, 172124, 510945, 683069, 1194014, 11429195, 12623209, 125038076, 137661285, 262699361, 663060007, 925759368]; [n le 24 select I[n] else 170584*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved