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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).

%I A057045 #11 Aug 19 2016 04:32:04
%S A057045 2,1,2,3,4,5,6,8,10,12,16,20,25,32,41,52,66,85,107,137,174,221,281,
%T A057045 358,455,579,737,937,1192,1516,1929,2454,3121,3970,5050,6424,8171,
%U A057045 10394,13221,16818,21393,27212
%N 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).
%H A057045 Chai Wah Wu, <a href="/A057045/b057045.txt">Table of n, a(n) for n = 1..1000</a>
%F A057045 Round(sqrt(2*A000032(n-1))). - _Vladeta Jovovic_, Jun 14 2003
%o A057045 (Python)
%o A057045 from gmpy2 import isqrt_rem, lucas
%o A057045 def A057045(n):
%o A057045     i, j = isqrt_rem(2*lucas(n-1))
%o A057045     return int(i + int(4*(j-i) >= 1)) # _Chai Wah Wu_, Aug 16 2016
%Y A057045 Cf. A057062, A057048, A022846, A057057, A057054.
%K A057045 nonn
%O A057045 1,1
%A A057045 _Clark Kimberling_, Jul 30 2000