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A194920 a(n) = n - floor(n/sqrt(2)).

%I A194920 #30 Sep 08 2022 08:45:58
%S A194920 1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,10,10,10,
%T A194920 10,11,11,11,12,12,12,13,13,13,13,14,14,14,15,15,15,15,16,16,16,17,17,
%U A194920 17,17,18,18,18,19,19,19,20,20,20,20,21,21,21,22,22,22,22,23
%N A194920 a(n) = n - floor(n/sqrt(2)).
%C A194920 a(n) is the number of zeros in row n+1 in triangle A255195. - _Mats Granvik_, Feb 18 2015.
%H A194920 Vincenzo Librandi, <a href="/A194920/b194920.txt">Table of n, a(n) for n = 1..10000</a>
%t A194920 r = Sqrt[2]; p[n_] := n - Floor[n/r]
%t A194920 Table[p[n], {n, 1, 90}]  (* A194920 *)
%t A194920 g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
%t A194920 f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
%t A194920 f[20]  (* A194921 *)
%t A194920 row[n_] := Position[f[30], n];
%t A194920 u = TableForm[Table[row[n], {n, 1, 5}]]
%t A194920 v[n_, k_] := Part[row[n], k];
%t A194920 w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
%t A194920 {k, 1, n}]]  (* A194922 *)
%t A194920 q[n_] := Position[w, n]; Flatten[Table[q[n],
%t A194920 {n, 1, 80}]]   (* A195071 *)
%o A194920 (Magma) [n-Floor(n/Sqrt(2)): n in [1..80] ]; // _Vincenzo Librandi_, Sep 10 2011
%o A194920 (PARI) vector(100,n,n-floor(n/sqrt(2))) \\ _Derek Orr_, Feb 28 2015
%Y A194920 Cf. A194921.
%K A194920 nonn,easy
%O A194920 1,4
%A A194920 _Clark Kimberling_, Sep 08 2011