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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). 4

%I

%S 2,1,2,3,4,5,6,8,10,12,16,20,25,32,41,52,66,85,107,137,174,221,281,

%T 358,455,579,737,937,1192,1516,1929,2454,3121,3970,5050,6424,8171,

%U 10394,13221,16818,21393,27212

%N 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).

%H Chai Wah Wu, <a href="/A057045/b057045.txt">Table of n, a(n) for n = 1..1000</a>

%F Round(sqrt(2*A000032(n-1))). - _Vladeta Jovovic_, Jun 14 2003

%o (Python)

%o from gmpy2 import isqrt_rem, lucas

%o def A057045(n):

%o i, j = isqrt_rem(2*lucas(n-1))

%o return int(i + int(4*(j-i) >= 1)) # _Chai Wah Wu_, Aug 16 2016

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

%K nonn

%O 1,1

%A _Clark Kimberling_, Jul 30 2000

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Last modified February 22 09:17 EST 2020. Contains 332133 sequences. (Running on oeis4.)