The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A221763 Numbers m such that 11*m^2 - 7 is a square. 3
 1, 4, 16, 79, 319, 1576, 6364, 31441, 126961, 627244, 2532856, 12513439, 50530159, 249641536, 1008070324, 4980317281, 20110876321, 99356704084, 401209456096, 1982153764399, 8004078245599, 39543718583896, 159680355455884, 788892217913521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See the first comment of A221762. a(n) == 1 (mod 3). a(n+1)/a(n) tends alternately to (2+sqrt(11))^2/7 and (5+sqrt(11))^2/14; a(n+2)/a(n) tends to A176395^2/2. Positive values of x (or y) satisfying x^2 - 20xy + y^2 + 63 = 0. - Colin Barker, Feb 18 2014 LINKS Bruno Berselli, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (0,20,0,-1). FORMULA G.f.: x*(1+4*x-4*x^2-x^3)/(1-20*x^2+x^4). a(n) = ((11+2*t*(-1)^n)*(10-3*t)^floor(n/2)+(11-2*t*(-1)^n)*(10+3*t)^floor(n/2))/22, where t=sqrt(11). a(n)*a(n-3)-a(n-1)*a(n-2) = (3/2)*(9+(-1)^n). MAPLE A221763:=proc(q) local n; for n from 1 to q do if type(sqrt(11*n^2-7), integer) then print(n); fi; od; end: A221763(1000); # Paolo P. Lava, Feb 19 2013 MATHEMATICA LinearRecurrence[{0, 20, 0, -1}, {1, 4, 16, 79}, 24] CoefficientList[Series[(1 + 4 x - 4 x^2 - x^3)/(1 - 20 x^2 + x^4), {x, 0, 25}], x] (* Vincenzo Librandi, Aug 18 2013 *) PROG (MAGMA) m:=24; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+4*x-4*x^2-x^3)/(1-20*x^2+x^4))); (Maxima) makelist(expand(((11+2*sqrt(11)*(-1)^n)*(10-3*sqrt(11))^floor(n/2)+(11-2*sqrt(11)*(-1)^n)*(10+3*sqrt(11))^floor(n/2))/22), n, 1, 24); (MAGMA) I:=[1, 4, 16, 79]; [n le 4 select I[n] else 20*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Aug 18 2013 CROSSREFS Cf. A221762. Sequence in context: A014514 A000780 A002713 * A009318 A081682 A068788 Adjacent sequences:  A221760 A221761 A221762 * A221764 A221765 A221766 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 24 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)