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A138494 a and b are integers > 0 satisfying a^2 + b^2 = c^2. Sequence gives the number of choices for a and b between successive values of c. (Integer solutions for c (Pythagorean triples) are not included.)

%I A138494 #25 May 18 2024 14:52:07
%S A138494 1,3,4,5,7,8,11,13,13,14,15,19,20,21,21,23,26,29,29,28,35,33,34,37,37,
%T A138494 41,40,41,45,44,51,49,51,54,49,57,54,63,59,56,65,65,71,68,65,73,72,77,
%U A138494 75,79,78,75,83,80,91,85,89,88,91,95,94,97,99,96,99,99,105,110,103,109
%N A138494 a and b are integers > 0 satisfying a^2 + b^2 = c^2. Sequence gives the number of choices for a and b between successive values of c. (Integer solutions for c (Pythagorean triples) are not included.)
%C A138494 Also number of pairs (a, b) such that floor(s) = n and s > n where a and b are positive integers and s = sqrt(a^2 + b^2). - _David A. Corneth_, May 30 2019
%H A138494 David A. Corneth, <a href="/A138494/b138494.txt">Table of n, a(n) for n = 1..10000</a>
%F A138494 a(n) = A077770(n)/4 for n >= 1. - _Dimitri Papadopoulos_, May 29 2019
%o A138494 (QBasic) OPEN "PYTH.TXT" FOR OUTPUT AS #1
%o A138494 FOR C = 1 TO 100
%o A138494 N = 0
%o A138494 FOR A = 1 TO C
%o A138494 FOR B = 1 TO C
%o A138494 D = SQR(A * A + B * B)
%o A138494 IF D > C AND D < C + 1 THEN N = N + 1
%o A138494 NEXT B
%o A138494 NEXT A
%o A138494 PRINT #1, N;
%o A138494 NEXT C
%o A138494 CLOSE
%o A138494 (PARI) a(n)={ cnt = 0; for( x = 1, n, for( y = floor( sqrt( n^2 - x^2) ), floor( sqrt( n^2 + 2*n + 1 - x^2) ), d = x^2 + y^2; if( sqrt(d) > n && sqrt(d) < n+1, cnt = cnt + 1); ) ); return(cnt);} /* _Dimitri Papadopoulos_, May 29 2019 */
%Y A138494 Cf. A077770.
%K A138494 easy,nonn
%O A138494 1,2
%A A138494 Rick Walcott (rick(AT)campbellsci.com), May 09 2008