A341250 -id:A341250 - cp's OEIS frontend

A341249 a(n) = floor(rfloor(sn)), where r = 2 + sqrt(2) and s = sqrt(2).

3, 6, 13, 17, 23, 27, 30, 37, 40, 47, 51, 54, 61, 64, 71, 75, 81, 85, 88, 95, 99, 105, 109, 112, 119, 122, 129, 133, 139, 143, 146, 153, 157, 163, 167, 170, 177, 180, 187, 191, 194, 201, 204, 211, 215, 221, 225, 228, 235, 238, 245, 249, 252, 259, 262, 269

Offset: 1

Clark Kimberling, Feb 13 2021

Conjecture: 1 < r*s*n - a(n) < 2 for n >= 1.

Cf. A002193, A341239, A341250.

z = 140; r = 2 + Sqrt[2]; s = Sqrt[2]; f[x_] := Floor[r*Floor[s*x]];
Table[f[n], {n, 1, z}]
Table[Floor[(2+Sqrt[2])Floor[n Sqrt[2]]],{n,60}] (* Harvey P. Dale, Oct 09 2022 *)

A341248 a(n) = 5a(n-1) - 4a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.

Original entry on oeis.org

1, 4, 18, 86, 414, 1998, 9646, 46574, 224878, 1085806, 5242734, 25314158, 122227566, 590166894, 2849577838, 13758978926, 66434227054, 320772823918, 1548828203886, 7478404111214, 36108929260398, 174349333486446, 841833050987374, 4064729537895278

Offset: 1

Clark Kimberling, Feb 13 2021

Index entries for linear recurrences with constant coefficients, signature (5,0,-4).

Cf. A339828, A341240, A341250.

z = 40; r = Sqrt[2]; s = 2 + Sqrt[2]; f[x_] := Floor[r*Floor[s*x]];
Table[f[n], {n, 1, z}] (* A022804 *)
a[1] = 1; a[n_] := f[a[n - 1]];
t = Table[a[n], {n, 1, z}] (* A341248 *)

Let f(n) = floor(r*floor(s*n)) = A022804(n), where r = sqrt(2) and s = r + 2. Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.

G.f.: x*(1 - x - 2*x^2)/(1 - 5*x + 4*x^3). - Stefano Spezia, Feb 13 2021

cp's OEIS Frontend

A341249 a(n) = floor(rfloor(sn)), where r = 2 + sqrt(2) and s = sqrt(2).

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A341248 a(n) = 5a(n-1) - 4a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.

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cp's OEIS Frontend

A341249 a(n) = floor(r*floor(s*n)), where r = 2 + sqrt(2) and s = sqrt(2).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A341248 a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A341249 a(n) = floor(rfloor(sn)), where r = 2 + sqrt(2) and s = sqrt(2).

A341248 a(n) = 5a(n-1) - 4a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.