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, 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

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

David A. Corneth, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A138491 A138492 A138493 * A138495 A138496 A138497

Keyword

easy,nonn

Author

Rick Walcott (rick(AT)campbellsci.com), May 09 2008

Status

approved