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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. 4
113, 3473, 104161, 3121441, 93539153, 2803053233, 83998057921, 2517138684481, 75430162476593, 2260387735613393, 67736201905925281, 2029825669442145121, 60827033881358428433, 1822781190771310707953, 54622608689257962810241, 1636855479486967573599361 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)