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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
OFFSET
1,1
COMMENTS
For the first of the corresponding seven consecutive positive integers, see A262074.
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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 10 2015
STATUS
approved