A341250 a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 3, a(3) = 13.

1, 3, 13, 61, 293, 1413, 6821, 32933, 159013, 767781, 3707173, 17899813, 86427941, 417311013, 2014955813, 9729067301, 46976092453, 226820639013, 1095186925861, 5288030259493, 25532868741413, 123283596003621, 595265858980133, 2874197819935013

Offset

1,2

Links

Table of n, a(n) for n=1..24.

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

Formula

Let f(n) = floor(r*floor(s*n)) = A341249(n), where r = 2 + sqrt(2) and s = sqrt(2). Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.

a(n) = (A218989(n-2) + 1)/2. - Hugo Pfoertner, Feb 13 2021

G.f.: x*(-2*x^2 - 2*x + 1)/(4*x^3 - 5*x + 1). - Chai Wah Wu, Feb 15 2021

Mathematica

z = 40; r = 2 + Sqrt[2]; s = Sqrt[2]; f[x_] := Floor[r*Floor[s*x]];
Table[f[n], {n, 1, z}] (* A341249 *)
a[1] = 1; a[n_] := f[a[n - 1]];
Table[a[n], {n, 1, z}] (* A341250 *)

Crossrefs

Cf. A218989, A339828, A341240, A341249.

Sequence in context: A319924 A108143 A101368 * A026704 A046748 A256333

Adjacent sequences: A341247 A341248 A341249 * A341251 A341252 A341253

Keyword

nonn,easy

Author

Clark Kimberling, Feb 13 2021

Status

approved