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A261972
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The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.
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3
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25, 361, 5041, 70225, 978121, 13623481, 189750625, 2642885281, 36810643321, 512706121225, 7141075053841, 99462344632561, 1385331749802025, 19295182152595801, 268747218386539201, 3743165875258953025, 52135575035238803161, 726154884618084291241
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OFFSET
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1,1
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COMMENTS
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For the first of the corresponding four consecutive positive integers, see A157088.
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LINKS
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FORMULA
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a(n) = 15*a(n-1)-15*a(n-2)+a(n-3) for n>3.
G.f.: -x*(x^2-14*x+25) / ((x-1)*(x^2-14*x+1)).
a(n) = (-2-(7-4*sqrt(3))^n*(-2+sqrt(3))+(2+sqrt(3))*(7+4*sqrt(3))^n)/2. - Colin Barker, Mar 05 2016
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EXAMPLE
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25 is in the sequence because 25^2 + 26^2 + 27^2 = 2030 = 21^2 + 22^2 + 23^2 + 24^2.
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PROG
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(PARI) Vec(-x*(x^2-14*x+25)/((x-1)*(x^2-14*x+1)) + O(x^40))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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