A261933 The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seventeen consecutive positive integers.

40, 91, 2743, 6364, 192004, 445423, 13437571, 31173280, 940438000, 2181684211, 65817222463, 152686721524, 4606265134444, 10685888822503, 322372742188651, 747859530853720, 22561485688071160, 52339481270937931, 1578981625422792583, 3663015829434801484

Offset

1,1

Comments

For the first of the corresponding seventeen consecutive positive integers, see A261935.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,70,-70,-1,1).

Formula

G.f.: -x*(40*x^4+51*x^3-148*x^2+51*x+40) / ((x-1)*(x^4-70*x^2+1)).

Example

40 is in the sequence because 40^2 + 41^2 = 5^2 + 6^2 + ... + 21^2.

Mathematica

LinearRecurrence[{1, 70, -70, -1, 1}, {40, 91, 2743, 6364, 192004}, 20] (* Harvey P. Dale, Oct 17 2015 *)

Prog

(PARI) Vec(-x*(40*x^4+51*x^3-148*x^2+51*x+40)/((x-1)*(x^4-70*x^2+1)) + O(x^40))

Crossrefs

Cf. A001652, A031138, A261932, A261934, A261935.

Sequence in context: A044559 A092613 A005930 * A036194 A023695 A038466

Adjacent sequences: A261930 A261931 A261932 * A261934 A261935 A261936

Keyword

nonn,easy

Author

Colin Barker, Sep 06 2015

Status

approved