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A262139
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The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
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2
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22, 145, 862, 5041, 29398, 171361, 998782, 5821345, 33929302, 197754481, 1152597598, 6717831121, 39154389142, 228208503745, 1330096633342, 7752371296321, 45184131144598, 263352415571281, 1534930362283102, 8946229758127345, 52142448186480982
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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 nine consecutive positive integers, see A262140.
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LINKS
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FORMULA
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a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.
G.f.: -x*(x^2-9*x+22) / ((x-1)*(x^2-6*x+1)).
a(n) = (-14+3*(3-2*sqrt(2))^(1+n)+3*(3+2*sqrt(2))^(1+n))/4. - Colin Barker, Mar 05 2016
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EXAMPLE
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22 is in the sequence because 22^2 + ... + 29^2 = 5244 = 20^2 + ... + 28^2.
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MATHEMATICA
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LinearRecurrence[{7, -7, 1}, {22, 145, 862}, 30] (* Harvey P. Dale, Apr 19 2016 *)
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PROG
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(PARI) Vec(-x*(x^2-9*x+22)/((x-1)*(x^2-6*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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