A262018 The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eleven consecutive positive integers.

28, 5308, 945148, 168231388, 29944242268, 5329906892668, 948693482652988, 168862110005339548, 30056506887467786908, 5349889363859260730428, 952250250260060942229628, 169495194656926988456143708, 30169192398682743884251350748, 5369946751770871484408284289788

Offset

1,1

Comments

For the first of the corresponding eleven consecutive positive integers, see A262019.

Links

Colin Barker, Table of n, a(n) for n = 1..444

Index entries for linear recurrences with constant coefficients, signature (179,-179,1).

Formula

a(n) = 179*a(n-1)-179*a(n-2)+a(n-3) for n>3.

G.f.: -4*x*(7*x^2+74*x+7) / ((x-1)*(x^2-178*x+1)).

Example

28 is in the sequence because 28^2 + ... + 32^2 = 4510 = 15^2 + ... + 25^2.

Mathematica

LinearRecurrence[{179, -179, 1}, {28, 5308, 945148}, 30] (* Harvey P. Dale, May 16 2019 *)

Prog

(PARI) Vec(-4*x*(7*x^2+74*x+7)/((x-1)*(x^2-178*x+1)) + O(x^20))

Crossrefs

Cf. A157096, A262017, A262019.

Sequence in context: A364516 A355999 A193985 * A131315 A200999 A221935

Adjacent sequences: A262015 A262016 A262017 * A262019 A262020 A262021

Keyword

nonn,easy

Author

Colin Barker, Sep 08 2015

Status

approved