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A006431
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Numbers that have a unique partition into a sum of four nonnegative squares.
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4
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0, 1, 2, 3, 5, 6, 7, 8, 11, 14, 15, 23, 24, 32, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| From a(16)=96 onwards, the terms of this sequence satisfy the third order recurrence relation a(n)=4a(n-3) [From Ant King (mathstutoring(AT)ntlworld.com), Aug 15 2010]
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REFERENCES
| Lehmer, D. H.; On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No.8, October 1948, pp. 476-481. [From Ant King (mathstutoring(AT)ntlworld.com), Aug 15 2010]
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LINKS
| Index entries for sequences related to sums of squares
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FORMULA
| Consists of 7 odd numbers plus 0 and numbers of forms 2*4^k, 6*4^k, 14*4^k, k >= 0.
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MATHEMATICA
| Select[Range[0, 3584], Length[PowersRepresentations[ #, 4, 2]]==1&] [From Ant King (mathstutoring(AT)ntlworld.com), Aug 15 2010]
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PROG
| (PARI) {a(n)=if(n<1, 0, if(n<14, [1, 2, 3, 5, 6, 7, 8, 11, 14, 15, 23, 24, 32] [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<15, [1, 2, 3, 5, 6, 7, 8, 11, 14, 15, 23, 24, 32] [n-1], [4, 7, 12][n%3+1]*2^(n\3*2-7)))} /* Michael Somos Apr 23 2006 */
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CROSSREFS
| {n | A002635(n) = 1}
A180149 [From Ant King (mathstutoring(AT)ntlworld.com), Aug 15 2010]
Sequence in context: A191893 A016741 A191167 * A151894 A028229 A104452
Adjacent sequences: A006428 A006429 A006430 * A006432 A006433 A006434
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David M. Bloom.
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999
Corrected by T. D. Noe (noe(AT)sspectra.com), Jun 15 2006
Definition revised by Ant King, May 06 2010
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