A262074 The first of seven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.

113, 3473, 104161, 3121441, 93539153, 2803053233, 83998057921, 2517138684481, 75430162476593, 2260387735613393, 67736201905925281, 2029825669442145121, 60827033881358428433, 1822781190771310707953, 54622608689257962810241, 1636855479486967573599361

Offset

1,1

Comments

For the first of the corresponding eight consecutive positive integers, see A262075.

Links

Colin Barker, Table of n, a(n) for n = 1..676

Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

Formula

a(n) = 31*a(n-1)-31*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x^2-30*x+113) / ((x-1)*(x^2-30*x+1)).

Example

113 is in the sequence because 113^2 + ... + 119^2 (7 terms) = 94220 = 105^2 + ... + 112^2 (8 terms).

Mathematica

LinearRecurrence[{31, -31, 1}, {113, 3473, 104161}, 20] (* Vincenzo Librandi, Sep 11 2015 *)

Prog

(PARI) Vec(-x*(x^2-30*x+113)/((x-1)*(x^2-30*x+1)) + O(x^20))
(Magma) I:=[113, 3473, 104161]; [n le 3 select I[n] else 31*Self(n-1)-31*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Cf. A262075, A262076, A262077.

Sequence in context: A187519 A301529 A008362 * A200854 A012031 A283781

Adjacent sequences: A262071 A262072 A262073 * A262075 A262076 A262077

Keyword

nonn,easy

Author

Colin Barker, Sep 10 2015

Status

approved