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 A257828 Positive integers whose square is the sum of 97 consecutive squares. 11
 679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831, 10253011689091642135, 24386783991798773338556, 58003955471481693294113311, 1287975802673112210113634031, 3063449905150311732357259611836, 7286414311424213782299531873117895 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positive integers x in the solutions to 2*x^2-194*y^2-18624*y-599072 = 0. LINKS Colin Barker, Table of n, a(n) for n = 1..370 Index entries for linear recurrences with constant coefficients, signature (0,0,125619266,0,0,-1). FORMULA a(n) = 125619266*a(n-3)-a(n-6). G.f.: -679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1). EXAMPLE 679 is in the sequence because 679^2 = 461041 = 15^2+16^2+...+111^2. MATHEMATICA LinearRecurrence[{0, 0, 125619266, 0, 0, -1}, {679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831}, 30] (* Vincenzo Librandi, May 11 2015 *) Rest[CoefficientList[Series[-679x(x-1)(x^4+2277x^3+5415742x^2+ 2277x+1)/ (x^6-125619266x^3+1), {x, 0, 15}], x]] (* Harvey P. Dale, Aug 02 2021 *) PROG (PARI) Vec(-679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1) + O(x^100)) (MAGMA) I:=[679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831]; [n le 6 select I[n] else 125619266*Self(n-3)-Self(n-6): n in [1..20]]; // Vincenzo Librandi, May 11 2015 CROSSREFS Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257826, A257827. Sequence in context: A164650 A200828 A097772 * A253695 A253702 A235013 Adjacent sequences:  A257825 A257826 A257827 * A257829 A257830 A257831 KEYWORD nonn,easy AUTHOR Colin Barker, May 10 2015 STATUS approved

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Last modified May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)