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Search: id:A016850
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| 0, 25, 100, 225, 400, 625, 900, 1225, 1600, 2025, 2500, 3025, 3600, 4225, 4900, 5625, 6400, 7225, 8100, 9025, 10000, 11025, 12100, 13225, 14400, 15625, 16900, 18225, 19600, 21025, 22500, 24025, 25600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If we define C(n)=(5*n)^2 (n>0), the sequence is the first "square-sequence" such that for every n there exists p such that : C(n)=C(p)+C(p+n). We observe in fact that p=3n because 25=3^2+4^2. The sequence without 0 is linked with the first nontrivial solution (trivial: n^2=0^2+n^2) of the equation X^2=2Y^2+2n^2 where X=2*k and Y=2*p+n which is equivalent to k^2=p^2+(p+n)^2 for n given. The second such "square-sequence" is (29*n)^2 (n>0) because 29^2=20^2+21^2 and with this relation we obtain (29*n)^2=(20*n)^2+(20n+n)^2. - Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 23 2007
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MAPLE
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with(finance):seq(add(cashflows([1, 1, 3], 0 ), k=1..n)^2, n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
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CROSSREFS
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Adjacent sequences: A016847 A016848 A016849 this_sequence A016851 A016852 A016853
Sequence in context: A063769 A099771 A134422 this_sequence A042220 A114254 A042222
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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