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Search: id:A115410
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| A115410 |
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Sequence of iterated sums of squares (1^2+2^2+3^2+...+n^2). |
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+0
1
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| 1, 55, 349074740, 7458911738724515315524082613205180, 159232823342755035454279356693126603659457648808279391910878167820461916066223383414616137125812767424153893199341493609630
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OFFSET
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1,2
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COMMENT
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Can be understood as generalized iterated square pyramidal numbers. The growth of the sequence is bounded by O(n^3^n/3^(n/2)). This can be derived from the growth O(n^3/3) of the power two sum (1^2+2^2+3^2+...+n^2) by iteration.
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FORMULA
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Let T(n):=sum{k^2|k=1...n}; we define a(1):=T(1), a(2):=T(T(2)) etc., a(n):=T(T(T(...T(n))...))).
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EXAMPLE
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a(2)=T(T(2))=T(5)=55;
a(3)=T(T(T(3)))=T(T(14)=T(1015)=349074740.
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CROSSREFS
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Cf. A000330, A099129.
Adjacent sequences: A115407 A115408 A115409 this_sequence A115411 A115412 A115413
Sequence in context: A027580 A046194 A093255 this_sequence A036197 A107676 A005932
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 22 2006
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