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Products of Wythoff pairs: [n*r]*[n*r^2], where [] is the floor function and r is the golden ratio, (1+sqrt(5))/2.
1

%I #13 Aug 29 2022 20:37:44

%S 2,15,28,60,104,135,198,240,322,416,476,589,714,792,936,1025,1188,

%T 1363,1470,1664,1782,1995,2220,2356,2600,2856,3010,3285,3450,3744,

%U 4050,4233,4558,4895,5096,5452,5664,6039,6426,6656,7062,7303,7728,8165,8424,8880

%N Products of Wythoff pairs: [n*r]*[n*r^2], where [] is the floor function and r is the golden ratio, (1+sqrt(5))/2.

%F a(n) = A000201(n) * A001950(n) = floor(n*r)*(n+floor(n*r)), where r=(1+sqrt(5))/2.

%e Wythoff pairs: (1,2), (3,5), (4,7), (6,10),..., so that

%e A075312 = (1*2, 3*5, 4*7, 6*10,...).

%o (Python)

%o from math import isqrt

%o def A075312(n): return (lambda m: m*(m+n))(n+isqrt(5*n**2)>>1) # _Chai Wah Wu_, Aug 29 2022

%Y The pairs are (A000201(n), A001950(n)). The sum is given by A003623.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 13 2002