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!)
A257825 Positive integers whose square is the sum of 74 consecutive squares. 3
2257, 2849, 21941, 27713, 604765, 763865, 16669573, 21054961, 162316669, 205018517, 4474051285, 5651073085, 123321498797, 155764598629, 1200818695321, 1516726961053, 33099030801665, 41806637918965, 912332431430633, 1152346479602381, 8883656545668089 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-148*y^2-10804*y-264698 = 0.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,7398,0,0,0,0,0,-1).
FORMULA
a(n) = 7398*a(n-6)-a(n-12).
G.f.: -37*x*(5*x^11+5*x^10+61*x^9+77*x^8+593*x^7+749*x^6-20645*x^5-16345*x^4-749*x^3-593*x^2-77*x-61) / ((x^6-86*x^3-1)*(x^6+86*x^3-1)).
EXAMPLE
2257 is in the sequence because 2257^2 = 5094049 = 225^2+226^2+...+298^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 7398, 0, 0, 0, 0, 0, -1}, {2257, 2849, 21941, 27713, 604765, 763865, 16669573, 21054961, 162316669, 205018517, 4474051285, 5651073085}, 40] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI) Vec(-37*x*(5*x^11+5*x^10+61*x^9+77*x^8+593*x^7+749*x^6-20645*x^5-16345*x^4-749*x^3-593*x^2-77*x-61) / ((x^6-86*x^3-1)*(x^6+86*x^3-1)) + O(x^100))
(Magma) I:=[2257, 2849, 21941, 27713, 604765, 763865, 16669573, 21054961, 162316669, 205018517, 4474051285, 5651073085]; [n le 12 select I[n] else 7398*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
Sequence in context: A068754 A222951 A035873 * A251678 A231245 A046168
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 March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)