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A189173
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Integers m such that m^3 is the sum of squares of m consecutive integers.
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0
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0, 1, 47, 2161, 99359, 4568353, 210044879, 9657496081, 444034774847, 20415942146881, 938689303981679, 43159292041010353, 1984388744582494559, 91238722958753739361, 4194996867358089516047, 192878617175513363998801, 8868221393206256654428799, 407745305470312292739725953, 18747415830241159209372965039
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OFFSET
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1,3
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LINKS
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Problems in Elementary Number Theory (PEN), Problem P 15, Art of Problem Solving website, 2007.
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FORMULA
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For n>3, a(n) = 46*a(n-1) - a(n-2).
a(n) = ((-517+90*sqrt(33))*(23+4*sqrt(33))^n-(517+90*sqrt(33))*(23-4*sqrt(33))^n)/22 for n>1, a(1)=0. - Bruno Berselli, May 31 2011
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MATHEMATICA
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LinearRecurrence[{46, -1}, {0, 1, 47}, 19] (* a(1) prepended by Georg Fischer, Apr 03 2019 *)
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PROG
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(Maxima) makelist(if n=1 then 0 else expand(((90*sqrt(33)-517)*(23+4*sqrt(33))^n-(90*sqrt(33)+517)*(23-4*sqrt(33))^n)/22), n, 1, 19); /* Bruno Berselli, May 31 2011 */
(PARI) x='x+O('x^19); Vec(x^2*(1+x)/(1-46*x+x^2)) \\ Georg Fischer, Apr 03 2019
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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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