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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.
3
61, 1381, 30361, 666601, 14634901, 321301261, 7053992881, 154866542161, 3400009934701, 74645352021301, 1638797734533961, 35978904807725881, 789897108035435461, 17341757471971854301, 380728767275345359201, 8358691122585626048161, 183510475929608427700381
OFFSET
1,1
COMMENTS
For the first of the corresponding six consecutive positive integers, see A157096.
FORMULA
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)).
EXAMPLE
61 is in the sequence because 61^2 + ... + 65^2 = 19855 = 55^2 + ... + 60^2.
PROG
(PARI) Vec(-x*(x^2-22*x+61)/((x-1)*(x^2-22*x+1)) + O(x^40))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 08 2015
STATUS
approved