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A000534
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Numbers that are not the sum of 4 nonzero squares.
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6
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0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41, 56, 96, 128, 224, 384, 512, 896, 1536, 2048, 3584, 6144, 8192, 14336, 24576, 32768, 57344, 98304, 131072, 229376, 393216, 524288, 917504, 1572864, 2097152, 3670016, 6291456, 8388608, 14680064
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OFFSET
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1,3
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COMMENTS
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For n > 15, a(n) = A006431(n-1). - Thomas Ordowski, Nov 18 2012
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REFERENCES
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J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 140.
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 3, pp. 74-75.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
Index entries for sequences related to sums of squares
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FORMULA
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Consists of the numbers 0, 1, 3, 5, 9, 11, 17, 29, 41, 2*4^m, 6*4^m and 14*4^m (m >= 0). Compare A123069.
From 224 on, a(n) = 4*a(n-3).
Numbers n such that A025428(n) = 0.
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MATHEMATICA
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q=22; lst={}; Do[Do[Do[Do[z=a^2+b^2+c^2+d^2; If[z<=q^2+3, AppendTo[lst, z]], {d, q}], {c, q}], {b, q}], {a, q}]; lst1=Union@lst lst={}; Do[AppendTo[lst, n], {n, q^2+3}]; lst2=lst Complement[lst2, lst1] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)
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PROG
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(PARI) for(n=1, 224, if(sum(a=1, n, sum(b=1, a, sum(c=1, b, sum(d=1, c, if(a^2+b^2+c^2+d^2-n, 0, 1)))))==0, print1(n, ", ")))
(PARI) {a(n)=if(n<1, 0, if(n<15, [1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41][n], [4, 7, 12][(n+1)%3+1]*2^((n+1)\3*2-7)))} /* Michael Somos, Apr 08 2006 */
(PARI) {a(n)=if(n<2, 0, if(n<16, [1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41][n-1], [4, 7, 12][n%3+1]*2^(n\3*2-7)))} /* Michael Somos, Apr 23 2006 */
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CROSSREFS
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Cf. A123069, A000414 (complement).
Sequence in context: A147855 A027563 A219729 * A136112 A127936 A096276
Adjacent sequences: A000531 A000532 A000533 * A000535 A000536 A000537
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KEYWORD
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nonn,easy,nice,changed
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AUTHOR
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N. J. A. Sloane and J. H. Conway (conway(AT)math.princeton.edu)
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STATUS
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approved
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