A390564 Upper (1/5,1/2) midsequence of (3^n) and (5*n); see Comments.

1, 3, 6, 11, 23, 57, 156, 450, 1326, 3952, 11827, 35448, 106309, 318887, 956618, 2869807, 8609371, 25828061, 77484128, 232452326, 697356914, 2092070676, 6276211959, 18828635804, 56485907337, 169457721931, 508373165710, 1525119497043, 4575358491039

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)) = (1,3,6,11,23,57,156,450,1326,3952,11827,35448,106309).

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}, {1, 3, 6, 11, 23, 57, 156, 450, 1326, 3952, 11827, 35448, 106309}, 30]

Crossrefs

Cf. A000244, A008587, A389123, A390563.

Sequence in context: A051284 A319910 A369848 * A346050 A319636 A001867

Adjacent sequences: A390561 A390562 A390563 * A390565 A390566 A390567

Keyword

nonn,easy

Author

Clark Kimberling, Nov 19 2025

Status

approved