A269451 The first of 50 consecutive positive integers the sum of the squares of which is a square.

7, 28, 44, 67, 87, 124, 168, 287, 379, 512, 628, 843, 1099, 1792, 2328, 3103, 3779, 5032, 6524, 10563, 13687, 18204, 22144, 29447, 38143, 61684, 79892, 106219, 129183, 171748, 222432, 359639, 465763, 619208, 753052, 1001139, 1296547, 2096248, 2714784

Offset

1,1

Comments

Positive integers y in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.

Numbers n such that 40425 + 2450*n + 50*n^2 is a square. - Harvey P. Dale, Oct 22 2016

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,6,-6,0,0,0,0,-1,1).

Formula

G.f.: x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)).

Example

7 is in the sequence because sum(k=7, 56, k^2) = 60025 = 245^2.

Mathematica

Select[Range[3*10^6], IntegerQ[Sqrt[40425+2450#+50#^2]]&] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, -1, 1}, {7, 28, 44, 67, 87, 124, 168, 287, 379, 512, 628, 843, 1099}, 40] (* Harvey P. Dale, Oct 22 2016 *)

Prog

(PARI) Vec(x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)) + O(x^40))

Crossrefs

Cf. A001032, A001652, A094196, A106521, A257781, A269447, A269448, A269449.

Sequence in context: A015817 A103253 A321777 * A139607 A068206 A118120

Adjacent sequences: A269448 A269449 A269450 * A269452 A269453 A269454

Keyword

nonn,easy,less

Author

Colin Barker, Feb 27 2016

Status

approved