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a(n) = n^2 + q*(q + 1), where q = floor(n*(1 + sqrt(5))/2) = A000201(n).
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%I #21 Mar 21 2024 12:33:39

%S 3,16,29,58,97,126,181,220,291,372,427,524,631,702,825,906,1045,1194,

%T 1291,1456,1563,1744,1935,2058,2265,2482,2621,2854,3003,3252,3511,

%U 3676,3951,4236,4417,4718,4909,5226,5553,5760,6103,6320,6679,7048,7281,7666,8061,8310

%N a(n) = n^2 + q*(q + 1), where q = floor(n*(1 + sqrt(5))/2) = A000201(n).

%H Paolo Xausa, <a href="/A371382/b371382.txt">Table of n, a(n) for n = 1..10000</a>

%t Array[#^2 + Block[{q = Floor[# * GoldenRatio]}, q * (q + 1)] &, 100]

%o (Python)

%o from math import isqrt

%o def A371382(n): return n**2+(q:=n+isqrt(5*n**2)>>1)*(q+1) # _Chai Wah Wu_, Mar 21 2024

%Y Main diagonal of A295573.

%Y Cf. A000201, A001622, A101332, A101863, A101867, A371381.

%K nonn,easy

%O 1,1

%A _Paolo Xausa_, Mar 20 2024