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A031138
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1^5+2^5+...+n^5 is a square.
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5
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1, 13, 133, 1321, 13081, 129493, 1281853, 12689041, 125608561, 1243396573, 12308357173, 121840175161, 1206093394441, 11939093769253, 118184844298093
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Partial sums of A004291 or convolution of A040000 with A054320. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009]
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LINKS
| Eric Weisstein's World of Mathematics, Hex Number
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FORMULA
| a(n) =11*(a(n-1)-a(n-2)) + a(n-3); a(n)=-1/2+((3-sqrt(6))/4)*(5+2sqrt(6))^n+((3+sqrt(6))/4)*(5-2sqrt(6))^n.
a(n)^2+(a(n)+1)^2=(b(n)-1)^2+b(n)^2+(b(n)+1)^2=c(n)=3d(n)+2; where b(n) is A054320, c(n) is A007667 and d(n) is A006061
a(n) = 10*a(n-1) - a(n-2) + 4; a(0) = a(1) = 1. Also sum of first a(n) fifth powers is a square m^2, where m has factors A000217{a(n)} and A054320(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 08 2002
contfrac(sqrt(6)/A054320(n))[4]/2 - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Dec 02 2003
G.f.: x*(1+x)^2/)(1-x)*(x^2-10*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009]
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EXAMPLE
| a(2)=13 because 1^5+2^5+...13^5=1001^2; a(1)=1 because 1^5=1^2
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CROSSREFS
| Cf. A006061, A054320, A007667.
Sequence in context: A081042 A016153 A187732 * A097166 A073556 A154999
Adjacent sequences: A031135 A031136 A031137 * A031139 A031140 A031141
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KEYWORD
| easy,nonn
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AUTHOR
| Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net) entry revised Feb 27 2000
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