A341240 a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - 4*a(n-4) + 2*a(n-5) for n >= 7, where a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 12, a(5) = 38, a(6) = 127.

1, 2, 4, 12, 38, 127, 432, 1472, 5023, 17148, 58544, 199879, 682428, 2329952, 7954951, 27159900, 92729696, 316598983, 1080936540, 3690548192, 12600319687, 43020182364, 146880090080, 501479995591, 1712159802204, 5845679217632, 19958397266119, 68142230629212

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Index entries for linear recurrences with constant coefficients, signature (4,-2,1,-4,2).

Formula

Let f(n) = floor(r*floor(s*n)) = A184922(n), where r = 1 + sqrt(2) and s = sqrt(2). Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.

G.f.: x*(1 - 2*x - 2*x^2 - x^3 + x^5)/(1 - 4*x + 2*x^2 - x^3 + 4*x^4 - 2*x^5). - Stefano Spezia, Feb 11 2021

Mathematica

z = 50; r = 1 + Sqrt[2]; s = Sqrt[2]; f[x_] := Floor[r*Floor[s*x]];
Table[f[n], {n, 1, z}] (* A341239 *)
a[1] = 1; a[n_] := f[a[n - 1]];
Table[a[n], {n, 1, z}] (* A341240 *)
LinearRecurrence[{4, -2, 1, -4, 2}, {1, 2, 4, 12, 38, 127}, 30] (* Harvey P. Dale, Jun 14 2022 *)

Crossrefs

Cf. A184922, A339828, A341239.

Sequence in context: A149845 A217616 A149846 * A108532 A213058 A268069

Adjacent sequences: A341237 A341238 A341239 * A341241 A341242 A341243

Keyword

nonn,easy

Author

Clark Kimberling, Feb 07 2021

Status

approved