A390563 Lower (1/5,1/2) midsequence of (3^n) and (5*n); see Comments.

0, 2, 5, 10, 22, 56, 155, 449, 1325, 3951, 11826, 35447, 106308, 318886, 956617, 2869806, 8609370, 25828060, 77484127, 232452325, 697356913, 2092070675, 6276211958, 18828635803, 56485907336, 169457721930, 508373165709, 1525119497042, 4575358491038

Offset

0,2

Comments

Suppose that s = (s(n)) and t = (t(n)) are sequences of numbers and h > 0 and k > 0. The lower (h, k)-midsequence of s and t is floor(h*s + k*t); the upper (h, k)-midsequence of s and t is ceiling(h*s + k*t).

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (5,-8,8,-8,8,-8,8,-8,8,-8,8,-7,3).

Formula

a(n) = 5*a(n-1) - 8*a(n-2) + 8*a(n-3) - 8*a(n-4) + 8*a(n-5) - 8*a(n-6) + 8*a(n-7) - 8*a(n-8) + 8*a(n-9) - 8*a(n-10) + 8*a(n-11) - 7*a(n-12) + 3*a(n-13), with (a(0),...,a(12)) = (0, 2, 5, 10, 22, 56, 155, 449, 1325, 3951, 11826, 35447, 106308).

Example

s = A000244 = (1, 3, 9, 27, 81, 243, 729, ...).
t = A008587 = (0, 5, 10, 15, 20, 25, 30, ...).
u(n) = (0, 2, 5, 10, 22, 56, 155, 449, 1325, ...).
v(n) = (1, 3, 6, 11, 23, 57, 156, 450, 1326, ...).

Mathematica

s[n_] := 3^n ; t[n_] := 5 n;
u[n_] := Floor[(s[n]/5 + t[n]/3)]
v[n_] := Ceiling[(s[n]/5 + t[n]/3)]
Table[u[n], {n, 0, 60}]  (* A390563 *)
Table[v[n], {n, 0, 60}]  (* A390564 *)
(* Also *)
LinearRecurrence[{5, -8, 8, -8, 8, -8, 8, -8, 8, -8, 8, -7, 3}, {0, 2, 5, 10, 22, 56, 155, 449, 1325, 3951, 11826, 35447, 106308}, 30]

Crossrefs

Cf. A000244, A008587, A389123, A390564.

Sequence in context: A166300 A038149 A046745 * A198950 A379378 A015902

Adjacent sequences: A390560 A390561 A390562 * A390564 A390565 A390566

Keyword

nonn,easy

Author

Clark Kimberling, Nov 17 2025

Status

approved