A261974 The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers.

67, 3307, 152275, 7001563, 321919843, 14801311435, 680538406387, 31289965382587, 1438657869192835, 66146972017488043, 3041322054935257363, 139834667555004350875, 6429353385475264883107, 295610421064307180272267, 13591650015572655027641395

Offset

1,1

Comments

For the first of the corresponding three consecutive positive integers, see A261973.

Links

Colin Barker, Table of n, a(n) for n = 1..601

Index entries for linear recurrences with constant coefficients, signature (47,-47,1).

Formula

a(n) = 47*a(n-1)-47*a(n-2)+a(n-3) for n>3.

G.f.: x*(5*x^2-158*x-67) / ((x-1)*(x^2-46*x+1)).

a(n) = -5+3*sqrt(3/11)*(23+4*sqrt(33))^(-n)*(-1+(23+4*sqrt(33))^(2*n)). - Colin Barker, Mar 03 2016

Example

67 is in the sequence because 67^2 + ... + 77^2 = 57134 = 137^2 + 138^2 + 139^2.

Mathematica

LinearRecurrence[{47, -47, 1}, {67, 3307, 152275}, 20] (* Harvey P. Dale, Jul 02 2016 *)

Prog

(PARI) Vec(x*(5*x^2-158*x-67)/((x-1)*(x^2-46*x+1)) + O(x^40))

Crossrefs

Cf. A157088, A261972, A261973.

Sequence in context: A069397 A103727 A120663 * A328353 A078989 A156121

Adjacent sequences: A261971 A261972 A261973 * A261975 A261976 A261977

Keyword

nonn,easy

Author

Colin Barker, Sep 07 2015

Status

approved