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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.) 1
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, 41, 40, 41, 45, 44, 51, 49, 51, 54, 49, 57, 54, 63, 59, 56, 65, 65, 71, 68, 65, 73, 72, 77, 75, 79, 78, 75, 83, 80, 91, 85, 89, 88, 91, 95, 94, 97, 99, 96, 99, 99, 105, 110, 103, 109 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
a(n) = A077770(n)/4 for n >= 1. - Dimitri Papadopoulos, May 29 2019
PROG
(QBasic) OPEN "PYTH.TXT" FOR OUTPUT AS #1
FOR C = 1 TO 100
N = 0
FOR A = 1 TO C
FOR B = 1 TO C
D = SQR(A * A + B * B)
IF D > C AND D < C + 1 THEN N = N + 1
NEXT B
NEXT A
PRINT #1, N;
NEXT C
CLOSE
(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 */
CROSSREFS
Cf. A077770.
Sequence in context: A359822 A257408 A131613 * A285531 A111801 A108372
KEYWORD
easy,nonn
AUTHOR
Rick Walcott (rick(AT)campbellsci.com), May 09 2008
STATUS
approved

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Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)