A262017 The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of six consecutive positive integers.

61, 1381, 30361, 666601, 14634901, 321301261, 7053992881, 154866542161, 3400009934701, 74645352021301, 1638797734533961, 35978904807725881, 789897108035435461, 17341757471971854301, 380728767275345359201, 8358691122585626048161, 183510475929608427700381

Offset

1,1

Comments

For the first of the corresponding six consecutive positive integers, see A157096.

Links

Colin Barker, Table of n, a(n) for n = 1..744

Index entries for linear recurrences with constant coefficients, signature (23,-23,1).

Formula

a(n) = 23*a(n-1)-23*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x^2-22*x+61) / ((x-1)*(x^2-22*x+1)).

Example

61 is in the sequence because 61^2 + ... + 65^2 = 19855 = 55^2 + ... + 60^2.

Prog

(PARI) Vec(-x*(x^2-22*x+61)/((x-1)*(x^2-22*x+1)) + O(x^40))

Crossrefs

Cf. A157096, A262018, A262019.

Cf. A027578, A027865.

Sequence in context: A152868 A218112 A154428 * A060061 A000507 A350974

Adjacent sequences: A262014 A262015 A262016 * A262018 A262019 A262020

Keyword

nonn,easy

Author

Colin Barker, Sep 08 2015

Status

approved