A057045 Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; ...; the n-th Lucas number is in antidiagonal a(n).

2, 1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 41, 52, 66, 85, 107, 137, 174, 221, 281, 358, 455, 579, 737, 937, 1192, 1516, 1929, 2454, 3121, 3970, 5050, 6424, 8171, 10394, 13221, 16818, 21393, 27212

Offset: 1

Author

Clark Kimberling, Jul 30 2000

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057062, A057048, A022846, A057057, A057054.

Programs

Python

from gmpy2 import isqrt_rem, lucas
def A057045(n):
    i, j = isqrt_rem(2*lucas(n-1))
    return int(i + int(4*(j-i) >= 1)) # Chai Wah Wu, Aug 16 2016

Formula

Round(sqrt(2*A000032(n-1))). - Vladeta Jovovic, Jun 14 2003