login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

License Agreements, Terms of Use, Privacy Policy. .

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