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Search: id:A091143
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| A091143 |
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Number of Pythagorean triples mod 2^n; i.e. number of solutions to x^2 + y^2 = z^2 mod 2^n. |
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+0
2
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| 1, 4, 24, 96, 448, 1792, 7680, 30720, 126976, 507904, 2064384, 8257536, 33292288, 133169152, 534773760, 2139095040, 8573157376, 34292629504, 137304735744, 549218942976, 2197949513728, 8791798054912
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This Mathematica program is much more efficient than the one given in A062775.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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a(2k) = (2^(k+1)-1) 2^(3k), a(2k-1) = (2^k-1) 2^(3k-1)
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MATHEMATICA
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Table[n = 2^k; b = Table[0, {n}]; Do[ b[[1 + Mod[i^2, n]]]++, {i, 0, n - 1}]; cnt = 0; Do[m = x^2 + y^2; cnt = cnt + b[[1 + Mod[m, n]]], {x, 0, n - 1}, {y, 0, n - 1}]; cnt, {k, 0, 13}]
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CROSSREFS
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Cf. A062775 (number of Pythagorean triples mod n).
Sequence in context: A119878 A054603 A100381 this_sequence A119920 A100738 A139238
Adjacent sequences: A091140 A091141 A091142 this_sequence A091144 A091145 A091146
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Dec 22 2003
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EXTENSIONS
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a(11) through a(13) from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 24 2003
More terms from T. D. Noe (noe(AT)sspectra.com), Feb 22 2007
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