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.
Original entry on oeis.org
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
-
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 *)
A341250
a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 3, a(3) = 13.
Original entry on oeis.org
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
-
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 *)
A341255
Let f(n) = floor(r*floor(r*n)) = A341254(n), where r = (2 + sqrt(5))/2. Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.
Original entry on oeis.org
1, 4, 16, 69, 309, 1385, 6212, 27866, 125008, 560793, 2515754, 11285842, 50629052, 227125366, 1018899829, 4570853893, 20505161277, 91987547377, 412662390616, 1851231536059, 8304750512850, 37255675336820, 167131492108634, 749763234780300, 3363488838254558
Offset: 1
-
z = 40; u = GoldenRatio;
r = u + 1/2; f[x_] := Floor[r*Floor[r*x]];
Table[f[n], {n, 1, z}] (* A341254 *)
a[1] = 1; a[n_] := f[a[n - 1]];
Table[a[n], {n, 1, z}] (* A341255 *)
A341248
a(n) = 5*a(n-1) - 4*a(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
-
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 *)
Showing 1-4 of 4 results.