Search: id:A091143
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%I A091143
%S A091143 1,4,24,96,448,1792,7680,30720,126976,507904,2064384,8257536,
%T A091143 33292288,133169152,534773760,2139095040,8573157376,34292629504,
%U A091143 137304735744,549218942976,2197949513728,8791798054912
%N A091143 Number of Pythagorean triples mod 2^n; i.e. number of solutions to x^2 
               + y^2 = z^2 mod 2^n.
%C A091143 This Mathematica program is much more efficient than the one given in 
               A062775.
%H A091143 T. D. Noe, <a href="b091143.txt">Table of n, a(n) for n=0..100</a>
%F A091143 a(2k) = (2^(k+1)-1) 2^(3k), a(2k-1) = (2^k-1) 2^(3k-1)
%t A091143 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}]
%Y A091143 Cf. A062775 (number of Pythagorean triples mod n).
%Y A091143 Sequence in context: A119878 A054603 A100381 this_sequence A119920 A100738 
               A139238
%Y A091143 Adjacent sequences: A091140 A091141 A091142 this_sequence A091144 A091145 
               A091146
%K A091143 nonn
%O A091143 0,2
%A A091143 T. D. Noe (noe(AT)sspectra.com), Dec 22 2003
%E A091143 a(11) through a(13) from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 24 
               2003
%E A091143 More terms from T. D. Noe (noe(AT)sspectra.com), Feb 22 2007

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