A257824 Positive integers whose square is the sum of 73 consecutive squares.

4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088, 85056113063608088, 486263602888235360, 32944848197744794640, 188344846763231651912, 388068345740467131839912, 2218576715650261475158640, 150310804012507009263599360

Offset

1,1

Comments

Positive integers x in the solutions to 2*x^2-146*y^2-10512*y-254040 = 0.

Links

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (0,0,0,4562498,0,0,0,-1).

Formula

a(n) = 4562498*a(n-4)-a(n-8).

G.f.: -584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)).

Example

4088 is in the sequence because 4088^2 = 16711744 = 442^2+443^2+...+514^2.

Mathematica

LinearRecurrence[{0, 0, 0, 4562498, 0, 0, 0, -1}, {4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088}, 40] (* Vincenzo Librandi, May 11 2015 *)

Prog

(PARI) Vec(-584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)) + O(x^100))
(Magma) I:=[4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088]; [n le 8 select I[n] else 4562498*Self(n-4)-Self(n-8): n in [1..20]]; // Vincenzo Librandi, May 11 2015

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823, A257825-A257828.

Sequence in context: A251005 A256028 A063889 * A024022 A145591 A103289

Adjacent sequences: A257821 A257822 A257823 * A257825 A257826 A257827

Keyword

nonn,easy

Author

Colin Barker, May 10 2015

Status

approved