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

1,1

Links

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A080915 A239484 A058714 * A237753 A058700 A220237

Adjacent sequences: A057042 A057043 A057044 * A057046 A057047 A057048

Keyword

nonn

Author

Clark Kimberling, Jul 30 2000

Status

approved