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

Author

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

Keywords

• easy
• nonn

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

Crossrefs

Cf. A077770.

Programs

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 */

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

Formula

a(n) = A077770(n)/4 for n >= 1. - Dimitri Papadopoulos, May 29 2019