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A262075 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers. 4
105, 3248, 97433, 2919840, 87497865, 2622016208, 78572988473, 2354567638080, 70558456154025, 2114399116982768, 63361415053329113, 1898728052482890720, 56898480159433392585, 1705055676730518886928, 51094771821756133215353, 1531138098975953477573760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the first of the corresponding seven consecutive positive integers, see A262074.

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.: 7*x*(x-15) / ((x-1)*(x^2-30*x+1)).

EXAMPLE

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

MATHEMATICA

LinearRecurrence[{31, -31, 1}, {105, 3248, 97433}, 20] (* Vincenzo Librandi, Sep 11 2015 *)

Table[1/4 (-14-(15-4 Sqrt[14])^n (7+2 Sqrt[14])+(-7+2 Sqrt[14]) (15+4 Sqrt[ 14])^n), {n, 2, 20}]//Simplify (* Harvey P. Dale, Aug 01 2019 *)

PROG

(PARI) Vec(7*x*(x-15)/((x-1)*(x^2-30*x+1)) + O(x^20))

(MAGMA) I:=[105, 3248, 97433]; [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. A262074, A262076, A262077.

Sequence in context: A220822 A166821 A166803 * A018233 A154633 A122814

Adjacent sequences:  A262072 A262073 A262074 * A262076 A262077 A262078

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 10 2015

STATUS

approved

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)