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Search: id:A130872
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| A130872 |
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Number of ways to write 8n - 1 as a sum of 7 (not necessarily distinct) odd perfect squares. |
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+0
1
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| 1, 1, 1, 2, 2, 2, 4, 4, 3, 5, 5, 5, 7, 7, 6, 9, 10, 8, 11, 11, 10, 15, 14, 12, 16, 17, 15, 19, 19, 17, 22, 24, 20, 25, 27, 23, 30, 29, 26, 32, 34, 30, 36, 38, 33, 40, 43, 37, 44, 47, 41, 50, 52, 45, 53, 55, 50, 58, 62, 54, 63, 70, 59, 68, 71, 64, 75, 79, 70, 79, 85, 77, 85, 89, 81
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Since all odd perfect squares are congruent to 1 mod 8, it is not possible to express any number congruent to 7 mod 8 as a sum of fewer than 7 odd perfect squares.
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EXAMPLE
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a(2) = 1 because 15 = 9 + 1 + 1 + 1 + 1 + 1 + 1 is the only such representation. a(4) = 2 because 31 = 25 + 1 + 1 + 1 + 1 + 1 + 1 = 9 + 9 + 9 + 1 + 1 + 1 + 1.
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MAPLE
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A130872recur := proc(n, jmin, N) local a, s ; if N =1 then if n mod 2 = 1 and issqr(n) and n>=jmin^2 then RETURN(1) ; else RETURN(0) ; fi ; else a := 0 ; for s from 2*floor(jmin/2)+1 to floor(sqrt(n)) by 2 do a := a+A130872recur(n-s^2, s, N-1) ; od ; RETURN(a) ; fi ; end: A130872 := proc(n) option remember: A130872recur(8*n-1, 1, 7) ; end: seq(A130872(n), n=1..100); - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2007
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CROSSREFS
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Adjacent sequences: A130869 A130870 A130871 this_sequence A130873 A130874 A130875
Sequence in context: A130453 A070705 A101909 this_sequence A087627 A096491 A106160
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KEYWORD
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nonn
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AUTHOR
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Joel Lewis (jblewis(AT)post.harvard.edu), Jul 24 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2007
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