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

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, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23

Offset: 1

Author

Clark Kimberling, Sep 08 2011

Keywords

• nonn
• easy

Comments

a(n) is the number of zeros in row n+1 in triangle A255195. - Mats Granvik, Feb 18 2015.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A194921.

Programs

Magma

[n-Floor(n/Sqrt(2)): n in [1..80] ]; // Vincenzo Librandi, Sep 10 2011

Mathematica

r = Sqrt[2]; p[n_] := n - Floor[n/r]
Table[p[n], {n, 1, 90}]  (* A194920 *)
g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]
f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]
f[20]  (* A194921 *)
row[n_] := Position[f[30], n];
u = TableForm[Table[row[n], {n, 1, 5}]]
v[n_, k_] := Part[row[n], k];
w = Flatten[Table[v[k, n - k + 1], {n, 1, 13},
{k, 1, n}]]  (* A194922 *)
q[n_] := Position[w, n]; Flatten[Table[q[n],
{n, 1, 80}]]   (* A195071 *)

PARI

vector(100,n,n-floor(n/sqrt(2))) \\ Derek Orr, Feb 28 2015