A262019 -id:A262019 - cp's OEIS frontend

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

Colin Barker, Sep 08 2015

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

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

Colin Barker, Table of n, a(n) for n = 1..744
Index entries for linear recurrences with constant coefficients, signature (23,-23,1).

Cf. A157096, A262018, A262019.

Cf. A027578, A027865.

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

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)).

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.

Original entry on oeis.org

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

Offset: 1

Colin Barker, Sep 08 2015

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

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

Colin Barker, Table of n, a(n) for n = 1..444
Index entries for linear recurrences with constant coefficients, signature (179,-179,1).

Cf. A157096, A262017, A262019.

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

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

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)).

cp's OEIS Frontend

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.

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