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a(n) = floor(n*r) + floor((n-2)*r) + floor((n-4)*r) + ... + floor(k*r), where r = 2^(1/2) and k = 0 if n is even, k = 1 if n is odd.
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%I #8 May 11 2024 16:35:28

%S 0,1,2,5,7,12,15,21,26,33,40,48,56,66,75,87,97,111,122,137,150,166,

%T 181,198,214,233,250,271,289,312,331,355,376,401,424,450,474,502,527,

%U 557,583,614,642,674,704,737,769,803,836,872,906,944,979,1018,1055,1095

%N a(n) = floor(n*r) + floor((n-2)*r) + floor((n-4)*r) + ... + floor(k*r), where r = 2^(1/2) and k = 0 if n is even, k = 1 if n is odd.

%H Paolo Xausa, <a href="/A129232/b129232.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = Sum_{k=0..n} A129231(k).

%t Accumulate[Block[{n = 0}, NestList[Floor[++n*Sqrt[2]] - # &, 0, 100]]] (* _Paolo Xausa_, May 11 2024 *)

%Y Partial sums of A129231.

%K nonn

%O 0,3

%A _Clark Kimberling_, Apr 04 2007