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

Author

Colin Barker, May 10 2015

Keywords

• nonn
• easy

Comments

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

Examples

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

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).

Crossrefs

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

Programs

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

Mathematica

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

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))

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)).